<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>34</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">V. Iverson</style></author><author><style face="normal" font="default" size="100%">S Vavasis</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Mean and Variance Estimation Complexity in Arbitrary Distributions via Wasserstein Minimization</style></title></titles><dates><year><style  face="normal" font="default" size="100%">10040</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://arxiv.org/abs/2501.10172</style></url></web-urls></urls><language><style face="normal" font="default" size="100%">eng</style></language></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Andersen Ang</style></author><author><style face="normal" font="default" size="100%">Hans De Sterck</style></author><author><style face="normal" font="default" size="100%">Stephen Vavasis</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">MGProx: A nonsmooth multigrid proximal gradient method with adaptive restriction for strongly convex optimization</style></title><secondary-title><style face="normal" font="default" size="100%">SIAM J. Optimization</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">Accepted</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://arxiv.org/abs/2302.04077</style></url></web-urls></urls><language><style face="normal" font="default" size="100%">eng</style></language></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Sahar Karimi</style></author><author><style face="normal" font="default" size="100%">Stephen A. Vavasis</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Nonlinear conjugate gradient for smooth convex functions</style></title><secondary-title><style face="normal" font="default" size="100%">Mathematical Programming - Computation</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">Accepted</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://arxiv.org/pdf/2111.11613.pdf</style></url></web-urls></urls><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;
	&lt;span dir=&quot;ltr&quot; role=&quot;presentation&quot; style=&quot;left:196.001px;top:508.207px;18.1818px;sans-serif;transform:scaleX(0.969669);&quot;&gt;The method of nonlinear conjugate gradients (NCG) is widely used in practice for &lt;/span&gt;&lt;span dir=&quot;ltr&quot; role=&quot;presentation&quot; style=&quot;left:168.801px;top:530.807px;18.1818px;sans-serif;transform:scaleX(1.01648);&quot;&gt;unconstrained optimization, but it satisfies weak complexity bounds at best when &lt;/span&gt;&lt;span dir=&quot;ltr&quot; role=&quot;presentation&quot; style=&quot;left:168.801px;top:553.407px;18.1818px;sans-serif;transform:scaleX(1.01581);&quot;&gt;applied to smooth convex functions.&lt;/span&gt;&lt;span dir=&quot;ltr&quot; role=&quot;presentation&quot; style=&quot;left:462.438px;top:553.407px;18.1818px;sans-serif;&quot;&gt; &lt;/span&gt;&lt;span dir=&quot;ltr&quot; role=&quot;presentation&quot; style=&quot;left:475.401px;top:553.407px;18.1818px;sans-serif;transform:scaleX(1.00372);&quot;&gt;In contrast, Nesterov’s accelerated gradient &lt;/span&gt;&lt;span dir=&quot;ltr&quot; role=&quot;presentation&quot; style=&quot;left:168.801px;top:576.007px;18.1818px;sans-serif;transform:scaleX(1.0179);&quot;&gt;(AG) method is optimal up to constant factors for this class.&lt;/span&gt;&lt;br role=&quot;presentation&quot;&gt;&amp;nbsp;
&lt;/p&gt;

&lt;p&gt;
	&lt;span dir=&quot;ltr&quot; role=&quot;presentation&quot; style=&quot;left:196.001px;top:598.607px;18.1818px;sans-serif;transform:scaleX(1.00215);&quot;&gt;However, when specialized to quadratic function, conjugate gradient is optimal &lt;/span&gt;&lt;span dir=&quot;ltr&quot; role=&quot;presentation&quot; style=&quot;left:168.801px;top:621.207px;18.1818px;sans-serif;transform:scaleX(0.975326);&quot;&gt;in a strong sense among function-gradient methods. Therefore, there is seemingly a &lt;/span&gt;&lt;span dir=&quot;ltr&quot; role=&quot;presentation&quot; style=&quot;left:168.801px;top:643.808px;18.1818px;sans-serif;transform:scaleX(1.01008);&quot;&gt;gap in the menu of available algorithms: NCG, the optimal algorithm for quadratic &lt;/span&gt;&lt;span dir=&quot;ltr&quot; role=&quot;presentation&quot; style=&quot;left:168.801px;top:666.407px;18.1818px;sans-serif;transform:scaleX(1.01626);&quot;&gt;functions that also exhibits good practical performance for general functions, has &lt;/span&gt;&lt;span dir=&quot;ltr&quot; role=&quot;presentation&quot; style=&quot;left:168.801px;top:688.808px;18.1818px;sans-serif;transform:scaleX(1.00265);&quot;&gt;poor complexity bounds compared to AG.&lt;/span&gt;&lt;br role=&quot;presentation&quot;&gt;&amp;nbsp;
&lt;/p&gt;

&lt;p&gt;
	&lt;span dir=&quot;ltr&quot; role=&quot;presentation&quot; style=&quot;left:196.001px;top:711.407px;18.1818px;sans-serif;transform:scaleX(1.00708);&quot;&gt;We propose an NCG method called C+AG (“conjugate plus accelerated gradi&lt;/span&gt;&lt;span dir=&quot;ltr&quot; role=&quot;presentation&quot; style=&quot;left:168.801px;top:734.008px;18.1818px;sans-serif;transform:scaleX(1.00552);&quot;&gt;ent”) to close this gap, that is, it is optimal for quadratic functions and still satisfies&lt;/span&gt;&lt;span dir=&quot;ltr&quot; role=&quot;presentation&quot; style=&quot;left:168.801px;top:756.607px;18.1818px;sans-serif;transform:scaleX(1.00344);&quot;&gt;the best possible complexity bound for more general smooth convex functions.&lt;/span&gt;&lt;span dir=&quot;ltr&quot; role=&quot;presentation&quot; style=&quot;left:802.637px;top:756.607px;18.1818px;sans-serif;&quot;&gt; &lt;/span&gt;&lt;span dir=&quot;ltr&quot; role=&quot;presentation&quot; style=&quot;left:813.601px;top:756.607px;18.1818px;sans-serif;transform:scaleX(1.35194);&quot;&gt;It &lt;/span&gt;&lt;span dir=&quot;ltr&quot; role=&quot;presentation&quot; style=&quot;left:168.801px;top:779.208px;18.1818px;sans-serif;transform:scaleX(1.01228);&quot;&gt;takes conjugate gradient steps until insufficient progress is made, at which time it &lt;/span&gt;&lt;span dir=&quot;ltr&quot; role=&quot;presentation&quot; style=&quot;left:168.801px;top:801.807px;18.1818px;sans-serif;transform:scaleX(1.01432);&quot;&gt;switches to accelerated gradient steps, and later retries conjugate gradient.&lt;/span&gt;&lt;span dir=&quot;ltr&quot; role=&quot;presentation&quot; style=&quot;left:781.837px;top:801.807px;18.1818px;sans-serif;&quot;&gt; &lt;/span&gt;&lt;span dir=&quot;ltr&quot; role=&quot;presentation&quot; style=&quot;left:796px;top:801.807px;18.1818px;sans-serif;transform:scaleX(1.00445);&quot;&gt;The &lt;/span&gt;&lt;span dir=&quot;ltr&quot; role=&quot;presentation&quot; style=&quot;left:168.801px;top:824.408px;18.1818px;sans-serif;transform:scaleX(1.03257);&quot;&gt;proposed method has the following theoretical properties: (i) It is identical to lin&lt;/span&gt;&lt;span dir=&quot;ltr&quot; role=&quot;presentation&quot; style=&quot;left:168.801px;top:847.008px;18.1818px;sans-serif;transform:scaleX(1.03235);&quot;&gt;ear conjugate gradient (and hence terminates finitely) if the objective function is &lt;/span&gt;&lt;span dir=&quot;ltr&quot; role=&quot;presentation&quot; style=&quot;left:168.801px;top:869.608px;18.1818px;sans-serif;transform:scaleX(1.06775);&quot;&gt;quadratic; (ii) Its running-time bound is&lt;/span&gt;&lt;span dir=&quot;ltr&quot; role=&quot;presentation&quot; style=&quot;left:498.965px;top:869.608px;18.1818px;sans-serif;&quot;&gt; &lt;/span&gt;&lt;span dir=&quot;ltr&quot; role=&quot;presentation&quot; style=&quot;left:506.601px;top:869.608px;18.1818px;sans-serif;&quot;&gt;O&lt;/span&gt;&lt;span dir=&quot;ltr&quot; role=&quot;presentation&quot; style=&quot;left:521px;top:869.608px;18.1818px;sans-serif;&quot;&gt;(&lt;/span&gt;&lt;span dir=&quot;ltr&quot; role=&quot;presentation&quot; style=&quot;left:528px;top:869.608px;18.1818px;sans-serif;&quot;&gt;ǫ&lt;/span&gt;&lt;span dir=&quot;ltr&quot; role=&quot;presentation&quot; style=&quot;left:535.399px;top:866.724px;13.2835px;sans-serif;&quot;&gt;−&lt;/span&gt;&lt;span dir=&quot;ltr&quot; role=&quot;presentation&quot; style=&quot;left:546.399px;top:866.724px;13.2835px;sans-serif;&quot;&gt;1&lt;/span&gt;&lt;span dir=&quot;ltr&quot; role=&quot;presentation&quot; style=&quot;left:553.399px;top:866.724px;13.2835px;sans-serif;&quot;&gt;/&lt;/span&gt;&lt;span dir=&quot;ltr&quot; role=&quot;presentation&quot; style=&quot;left:560.399px;top:866.724px;13.2835px;sans-serif;&quot;&gt;2&lt;/span&gt;&lt;span dir=&quot;ltr&quot; role=&quot;presentation&quot; style=&quot;left:568.399px;top:869.608px;18.1818px;sans-serif;transform:scaleX(1.03146);&quot;&gt;) gradient evaluations for an&lt;/span&gt;&lt;span dir=&quot;ltr&quot; role=&quot;presentation&quot; style=&quot;left:800.891px;top:869.608px;18.1818px;sans-serif;&quot;&gt; &lt;/span&gt;&lt;span dir=&quot;ltr&quot; role=&quot;presentation&quot; style=&quot;left:808.799px;top:869.608px;18.1818px;sans-serif;&quot;&gt;L&lt;/span&gt;&lt;span dir=&quot;ltr&quot; role=&quot;presentation&quot; style=&quot;left:821.199px;top:869.608px;18.1818px;sans-serif;&quot;&gt;-&lt;/span&gt;&lt;span dir=&quot;ltr&quot; role=&quot;presentation&quot; style=&quot;left:168.799px;top:892.208px;18.1818px;sans-serif;transform:scaleX(0.981741);&quot;&gt;smooth convex function, where&lt;/span&gt;&lt;span dir=&quot;ltr&quot; role=&quot;presentation&quot; style=&quot;left:414.872px;top:892.208px;18.1818px;sans-serif;&quot;&gt; &lt;/span&gt;&lt;span dir=&quot;ltr&quot; role=&quot;presentation&quot; style=&quot;left:420.599px;top:892.208px;18.1818px;sans-serif;&quot;&gt;ǫ&lt;/span&gt;&lt;span dir=&quot;ltr&quot; role=&quot;presentation&quot; style=&quot;left:427.963px;top:892.208px;18.1818px;sans-serif;&quot;&gt; &lt;/span&gt;&lt;span dir=&quot;ltr&quot; role=&quot;presentation&quot; style=&quot;left:433.799px;top:892.208px;18.1818px;sans-serif;transform:scaleX(1.0172);&quot;&gt;is the desired residual reduction, (iii) Its running-&lt;/span&gt;&lt;span dir=&quot;ltr&quot; role=&quot;presentation&quot; style=&quot;left:168.799px;top:914.808px;18.1818px;sans-serif;transform:scaleX(1.05746);&quot;&gt;time bound is&lt;/span&gt;&lt;span dir=&quot;ltr&quot; role=&quot;presentation&quot; style=&quot;left:283.163px;top:914.808px;18.1818px;sans-serif;&quot;&gt; &lt;/span&gt;&lt;span dir=&quot;ltr&quot; role=&quot;presentation&quot; style=&quot;left:291.8px;top:914.808px;18.1818px;sans-serif;&quot;&gt;O&lt;/span&gt;&lt;span dir=&quot;ltr&quot; role=&quot;presentation&quot; style=&quot;left:306.199px;top:914.808px;18.1818px;sans-serif;&quot;&gt;(&lt;/span&gt;&lt;span dir=&quot;ltr&quot; role=&quot;presentation&quot; style=&quot;left:313.199px;top:899.208px;18.1818px;sans-serif;&quot;&gt;√&lt;/span&gt;&lt;span dir=&quot;ltr&quot; role=&quot;presentation&quot; style=&quot;left:331.4px;top:914.807px;18.1818px;sans-serif;transform:scaleX(1.37594);&quot;&gt;L/ℓ&lt;/span&gt;&lt;span dir=&quot;ltr&quot; role=&quot;presentation&quot; style=&quot;left:360.364px;top:914.807px;18.1818px;sans-serif;&quot;&gt; &lt;/span&gt;&lt;span dir=&quot;ltr&quot; role=&quot;presentation&quot; style=&quot;left:363.4px;top:914.807px;18.1818px;sans-serif;transform:scaleX(1.03214);&quot;&gt;ln(1&lt;/span&gt;&lt;span dir=&quot;ltr&quot; role=&quot;presentation&quot; style=&quot;left:394.6px;top:914.807px;18.1818px;sans-serif;transform:scaleX(1.07892);&quot;&gt;/ǫ&lt;/span&gt;&lt;span dir=&quot;ltr&quot; role=&quot;presentation&quot; style=&quot;left:411px;top:914.807px;18.1818px;sans-serif;transform:scaleX(1.12492);&quot;&gt;)) if the function is both&lt;/span&gt;&lt;span dir=&quot;ltr&quot; role=&quot;presentation&quot; style=&quot;left:617.891px;top:914.807px;18.1818px;sans-serif;&quot;&gt; &lt;/span&gt;&lt;span dir=&quot;ltr&quot; role=&quot;presentation&quot; style=&quot;left:626.401px;top:914.807px;18.1818px;sans-serif;&quot;&gt;L&lt;/span&gt;&lt;span dir=&quot;ltr&quot; role=&quot;presentation&quot; style=&quot;left:638.801px;top:914.807px;18.1818px;sans-serif;transform:scaleX(1.00997);&quot;&gt;-smooth and&lt;/span&gt;&lt;span dir=&quot;ltr&quot; role=&quot;presentation&quot; style=&quot;left:740.892px;top:914.807px;18.1818px;sans-serif;&quot;&gt; &lt;/span&gt;&lt;span dir=&quot;ltr&quot; role=&quot;presentation&quot; style=&quot;left:749.201px;top:914.807px;18.1818px;sans-serif;&quot;&gt;ℓ&lt;/span&gt;&lt;span dir=&quot;ltr&quot; role=&quot;presentation&quot; style=&quot;left:756.802px;top:914.807px;18.1818px;sans-serif;transform:scaleX(1.00691);&quot;&gt;-strongly &lt;/span&gt;&lt;span dir=&quot;ltr&quot; role=&quot;presentation&quot; style=&quot;left:168.802px;top:937.207px;18.1818px;sans-serif;transform:scaleX(0.929556);&quot;&gt;convex.&lt;/span&gt;&lt;span dir=&quot;ltr&quot; role=&quot;presentation&quot; style=&quot;left:227.038px;top:937.207px;18.1818px;sans-serif;&quot;&gt; &lt;/span&gt;&lt;span dir=&quot;ltr&quot; role=&quot;presentation&quot; style=&quot;left:238.602px;top:937.207px;18.1818px;sans-serif;transform:scaleX(1.03115);&quot;&gt;We also conjecture and outline a proof that a variant of the method has &lt;/span&gt;&lt;span dir=&quot;ltr&quot; role=&quot;presentation&quot; style=&quot;left:168.802px;top:959.806px;18.1818px;sans-serif;transform:scaleX(1.07543);&quot;&gt;the property: (iv) It is&lt;/span&gt;&lt;span dir=&quot;ltr&quot; role=&quot;presentation&quot; style=&quot;left:346.965px;top:959.806px;18.1818px;sans-serif;&quot;&gt; &lt;/span&gt;&lt;span dir=&quot;ltr&quot; role=&quot;presentation&quot; style=&quot;left:352.802px;top:959.806px;18.1818px;sans-serif;&quot;&gt;n&lt;/span&gt;&lt;span dir=&quot;ltr&quot; role=&quot;presentation&quot; style=&quot;left:363.802px;top:959.806px;18.1818px;sans-serif;transform:scaleX(0.977373);&quot;&gt;-step quadratically convergent for a function whose second &lt;/span&gt;&lt;span dir=&quot;ltr&quot; role=&quot;presentation&quot; style=&quot;left:168.802px;top:982.407px;18.1818px;sans-serif;transform:scaleX(1.05225);&quot;&gt;derivative is smooth and invertible at the optimizer. Note that the bounds in (ii) &lt;/span&gt;&lt;span dir=&quot;ltr&quot; role=&quot;presentation&quot; style=&quot;left:168.802px;top:1005.01px;18.1818px;sans-serif;transform:scaleX(1.01929);&quot;&gt;and (iii) match AG and are the best possible, i.e., they match lower bounds up to &lt;/span&gt;&lt;span dir=&quot;ltr&quot; role=&quot;presentation&quot; style=&quot;left:168.802px;top:1027.61px;18.1818px;sans-serif;transform:scaleX(0.975541);&quot;&gt;constant factors for the classes of functions under consideration. On the other hand, &lt;/span&gt;&lt;span dir=&quot;ltr&quot; role=&quot;presentation&quot; style=&quot;left:168.802px;top:1050.21px;18.1818px;sans-serif;transform:scaleX(1.05112);&quot;&gt;(i) and (iv) match NCG.&lt;/span&gt;&lt;br role=&quot;presentation&quot;&gt;&amp;nbsp;
&lt;/p&gt;
</style></abstract></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>27</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Matthew Hough</style></author><author><style face="normal" font="default" size="100%">Stephen Vavasis</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">A Primal-Dual Frank-Wolfe Algorithm for Linear Programming</style></title></titles><dates><year><style  face="normal" font="default" size="100%">2024</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://arxiv.org/abs/2402.18514</style></url></web-urls></urls><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">We present two first-order primal-dual algorithms for solving saddle point formulations of linear programs, namely FWLP (Frank-Wolfe Linear Programming) and FWLP-P. The former iteratively applies the Frank-Wolfe algorithm to both the primal and dual of the saddle point formulation of a standard-form LP. The latter is a modification of FWLP in which regularizing perturbations are used in computing the iterates. We show that FWLP-P converges to a primal-dual solution with error&amp;nbsp;O(1/sqrt(k))&amp;nbsp;after&amp;nbsp;k&amp;nbsp;iterations, while no convergence guarantees are provided for FWLP. We also discuss the advantages of using FWLP and FWLP-P for solving very large LPs. In particular, we argue that only part of the matrix&amp;nbsp;A&amp;nbsp;is needed at each iteration, in contrast to other first-order methods.</style></abstract></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>27</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Walaa Moursi</style></author><author><style face="normal" font="default" size="100%">Viktor Pavlovic</style></author><author><style face="normal" font="default" size="100%">Stephen Vavasis</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Accelerated gradient descent: A guaranteed bound for a heuristic restart strategy</style></title></titles><dates><year><style  face="normal" font="default" size="100%">2023</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://arxiv.org/abs/2310.07674</style></url></web-urls></urls><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">The&amp;nbsp;O(1/k^2)&amp;nbsp;convergence rate in function value of accelerated gradient descent is optimal, but there are many modifications that have been used to speed up convergence in practice. Among these modifications are restarts, that is, starting the algorithm with the current iteration being considered as the initial point. We focus on the adaptive restart techniques introduced by O'Donoghue and Candès, specifically their gradient restart strategy. While the gradient restart strategy is a heuristic in general, we prove that applying gradient restarts preserves and in fact improves the&amp;nbsp;O(1/k^2)&amp;nbsp;bound, hence establishing function value convergence, for one-dimensional functions. Applications of our results to separable and nearly separable functions are presented.</style></abstract></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Levent Tunçel</style></author><author><style face="normal" font="default" size="100%">Stephen A. Vavasis</style></author><author><style face="normal" font="default" size="100%">Jingye Xu</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Computational complexity of decomposing a symmetric matrix as a sum of positive semidefinite and diagonal matrices</style></title><secondary-title><style face="normal" font="default" size="100%">Foundations of Computational Mathematics</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2023</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://arxiv.org/abs/2209.05678</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">2023</style></volume><pages><style face="normal" font="default" size="100%">1-47</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">We study several variants of decomposing a symmetric matrix into a sum of a low-rank positive semidefinite matrix and a diagonal matrix. Such decompositions have applications in factor analysis and they have been studied for many decades. On the one hand, we prove that when the rank of the positive semidefinite matrix in the decomposition is bounded above by an absolute constant, the problem can be solved in polynomial time. On the other hand, we prove that, in general, these problems as well as their certain approximation versions are all NP-hard. Finally, we prove that many of these low-rank decomposition problems are complete in the first-order theory of the reals; i.e., given any system of polynomial equations, we can write down a low-rank decomposition problem in polynomial time so that the original system has a solution iff our corresponding decomposition problem has a feasible solution of certain (lowest) rank.</style></abstract></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>27</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Tao Jiang</style></author><author><style face="normal" font="default" size="100%">Walaa Moursi</style></author><author><style face="normal" font="default" size="100%">Stephen Vavasis</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Range of the displacement operator of PDHG with applications to quadratic and conic programming</style></title></titles><dates><year><style  face="normal" font="default" size="100%">2023</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://arxiv.org/abs/2309.15009</style></url></web-urls></urls><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">Primal-dual hybrid gradient (PDHG) is a first-order method for saddle-point problems and convex programming introduced by Chambolle and Pock. Recently, Applegate et al.\ analyzed the behavior of PDHG when applied to an infeasible or unbounded instance of linear programming, and in particular, showed that PDHG is able to diagnose these conditions. Their analysis hinges on the notion of the infimal displacement vector in the closure of the range of the displacement mapping of the splitting operator that encodes the PDHG algorithm. In this paper, we develop a novel formula for this range using monotone operator theory. The analysis is then specialized to conic programming and further to quadratic programming (QP) and second-order cone programming (SOCP). A consequence of our analysis is that PDHG is able to diagnose infeasible or unbounded instances of QP and of the ellipsoid-separation problem, a subclass of SOCP.</style></abstract></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>27</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Tao Jiang</style></author><author><style face="normal" font="default" size="100%">Samuel Tang</style></author><author><style face="normal" font="default" size="100%">Stephen Vavasis</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Re-embedding data to strengthen recovery guarantees of clustering</style></title></titles><dates><year><style  face="normal" font="default" size="100%">2023</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://arxiv.org/abs/2301.10901</style></url></web-urls></urls><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">We propose a clustering method that involves chaining four known techniques into a pipeline yielding an algorithm with stronger recovery guarantees than any of the four components separately. Given n points in R d , the first component of our pipeline, which we call leapfrog distances, is reminiscent of density-based clustering, yielding an n × n distance matrix. The leapfrog distances are then translated to new embeddings using multidimensional scaling and spectral methods, two other known techniques, yielding new embeddings of the n points in R^d' , where d' satisfies d' &amp;lt;&amp;lt; d in general. Finally, sum-of-norms (SON) clustering is applied to the re-embedded points. Although the fourth step (SON clustering) can in principle be replaced by any other clustering method, our focus is on provable guarantees of recovery of underlying structure. Therefore, we establish that the re-embedding improves recovery SON clustering, since SON clustering is a well-studied method that already has provable guarantees.</style></abstract></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Xuan Vinh Doan</style></author><author><style face="normal" font="default" size="100%">Stephen A. Vavasis</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Low-rank matrix recovery with Ky Fan 2-k-norm</style></title><secondary-title><style face="normal" font="default" size="100%">Journal of Global Optimization</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2022</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://link.springer.com/article/10.1007/s10898-021-01031-0</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">82</style></volume><pages><style face="normal" font="default" size="100%">727-751</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">Low-rank matrix recovery problem is difficult due to its non-convex properties and it is usually solved using convex relaxation approaches. In this paper, we formulate the non-convex low-rank matrix recovery problem exactly using novel Ky Fan 2-&lt;i&gt;k&lt;/i&gt;-norm-based models. A general difference of convex functions algorithm (DCA) is developed to solve these models. A proximal point algorithm (PPA) framework is proposed to solve sub-problems within the DCA, which allows us to handle large instances. Numerical results show that the proposed models achieve high recoverability rates as compared to the truncated nuclear norm method and the alternating bilinear optimization approach. The results also demonstrate that the proposed DCA with the PPA framework is efficient in handling larger instances.</style></abstract></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Tao Jiang</style></author><author><style face="normal" font="default" size="100%">Stephen A Vavasis</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Certifying clusters from sum-of-norms clustering</style></title></titles><dates><year><style  face="normal" font="default" size="100%">2021</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://arxiv.org/abs/2006.11355</style></url></web-urls></urls><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">Sum-of-norms clustering is a clustering formulation based on convex optimization that automatically induces hierarchy. Multiple algorithms have been proposed to solve the optimization problem: subgradient descent by Hocking et al., ADMM and ADA by Chi and Lange, stochastic incremental algorithm by Panahi et al. and semismooth Newton-CG augmented Lagrangian method by Sun et al. All algorithms yield approximate solutions, even though an exact solution is demanded to determine the correct cluster assignment. The purpose of this paper is to close the gap between the output from existing algorithms and the exact solution to the optimization problem. We present a clustering test that identifies and certifies the correct cluster assignment from an approximate solution yielded by any primal-dual algorithm. Our certification validates clustering for both unit and multiplicative weights. The test may not succeed if the approximation is inaccurate. However, we show the correct cluster assignment is guaranteed to be certified by a primal-dual path following algorithm after sufficiently many iterations, provided that the model parameter &lt;span class=&quot;MathJax&quot; id=&quot;MathJax-Element-1-Frame&quot; tabindex=&quot;0&quot;&gt;&lt;nobr&gt;&lt;span class=&quot;math&quot; id=&quot;MathJax-Span-1&quot; style=&quot;width:0.738em;display:inline-block;&quot;&gt;&lt;span style=&quot;display:inline-block;position:relative;width:0.613em;height:0px;120%;&quot;&gt;&lt;span style=&quot;position:absolute;clip:rect(1.328em,1000.59em,2.402em,-1000em);top:-2.206em;left:0em;&quot;&gt;&lt;span class=&quot;mrow&quot; id=&quot;MathJax-Span-2&quot;&gt;&lt;span class=&quot;mi&quot; id=&quot;MathJax-Span-3&quot; style=&quot;MathJax_Math;font-style:italic;&quot;&gt;λ&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/nobr&gt;&lt;/span&gt; avoids a finite number of bad values. Numerical experiments are conducted on Gaussian mixture and half-moon data, which indicate that carefully chosen multiplicative weights increase the recovery power of sum-of-norms clustering.</style></abstract></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>47</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Jimit Majmudar</style></author><author><style face="normal" font="default" size="100%">Stephen Vavasis</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Provable overlapping community detection in weighted graphs</style></title><secondary-title><style face="normal" font="default" size="100%">Neural Information Processing Systems (NeurIPS)</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2020</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://proceedings.neurips.cc/paper/2020</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">2020</style></volume><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">Community detection is a widely-studied unsupervised learning problem in which the task is to group similar entities together based on observed pairwise entity interactions. This problem has applications in diverse domains such as social network analysis and computational biology. There is a significant amount of literature studying this problem under the assumption that the communities do not overlap. When the communities are allowed to overlap, often a pure nodes assumption is made, i.e. each community has a node that belongs exclusively to that community. This assumption, however, may not always be satisfied in practice. In this paper, we provide a provable method to detect overlapping communities in weighted graphs without explicitly making the pure nodes assumption. Moreover, contrary to most existing algorithms, our approach is based on convex optimization, for which many useful theoretical properties are already known. We demonstrate the success of our algorithm on artificial and real-world datasets</style></abstract></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Jiang, T.</style></author><author><style face="normal" font="default" size="100%">Vavasis, S.</style></author><author><style face="normal" font="default" size="100%">Zhai., C. W.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Recovery of a mixture of Gaussians by sum-of-norms clustering</style></title><secondary-title><style face="normal" font="default" size="100%">Journal of Machine Learning Research</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2020</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://jmlr.org/papers/volume21/19-218/19-218.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">21</style></volume><pages><style face="normal" font="default" size="100%">1-16</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;span style=&quot;left:183.208px;top:652.985px;16.6043px;sans-serif;transform:scaleX(0.984627);&quot;&gt;Sum-of-norms clustering is a method for assigning&lt;/span&gt;&lt;span style=&quot;left:553.975px;top:652.985px;16.6043px;sans-serif;&quot;&gt; n &lt;/span&gt;&lt;span style=&quot;left:569.58px;top:652.985px;16.6043px;sans-serif;transform:scaleX(1.02966);&quot;&gt;points in &lt;/span&gt;&lt;span style=&quot;left:639.063px;top:652.985px;16.6043px;sans-serif;&quot;&gt;R&lt;/span&gt;&lt;span style=&quot;left:653.383px;top:649.155px;11.623px;monospace;&quot;&gt;d &lt;/span&gt;&lt;span style=&quot;left:666.763px;top:652.985px;16.6043px;sans-serif;transform:scaleX(1.06375);&quot;&gt;to&lt;/span&gt;&lt;span style=&quot;left:687.16px;top:652.985px;16.6043px;sans-serif;&quot;&gt; K &lt;/span&gt;&lt;span style=&quot;left:708.088px;top:652.985px;16.6043px;sans-serif;transform:scaleX(0.965163);&quot;&gt;clusters, 1&lt;/span&gt;&lt;span style=&quot;left:786.105px;top:652.055px;16.6043px;sans-serif;&quot;&gt;≤&lt;/span&gt;&lt;span style=&quot;left:803.803px;top:652.985px;16.6043px;sans-serif;&quot;&gt;K&lt;/span&gt;&lt;span style=&quot;left:823.877px;top:652.055px;16.6043px;sans-serif;&quot;&gt;≤&lt;/span&gt;&lt;span style=&quot;left:183.208px;top:672.91px;16.6043px;sans-serif;&quot;&gt;n&lt;/span&gt;&lt;span style=&quot;left:193.175px;top:672.91px;16.6043px;sans-serif;transform:scaleX(0.949803);&quot;&gt;, using convex optimization. Recently, Panahi et al. (2017) proved that sum-of-norms &lt;/span&gt;&lt;span style=&quot;left:183.208px;top:692.837px;16.6043px;sans-serif;transform:scaleX(1.0181);&quot;&gt;clustering is guaranteed to recover a mixture of Gaussians under the restriction that the &lt;/span&gt;&lt;span style=&quot;left:183.208px;top:712.762px;16.6043px;sans-serif;transform:scaleX(0.945846);&quot;&gt;number of samples is not too large. The purpose of this note is to lift this restriction, &lt;/span&gt;&lt;span style=&quot;left:183.208px;top:732.687px;16.6043px;sans-serif;transform:scaleX(0.982827);&quot;&gt;that is, show that sum-of-norms clustering can recover a mixture of Gaussians even as the&lt;/span&gt;&lt;span style=&quot;left:183.208px;top:752.612px;16.6043px;sans-serif;transform:scaleX(0.947623);&quot;&gt; number of samples tends to infinity. Our proof relies on an interesting characterization &lt;/span&gt;&lt;span style=&quot;left:183.208px;top:772.537px;16.6043px;sans-serif;transform:scaleX(0.993851);&quot;&gt;of clusters computed by sum-of-norms clustering that was developed inside a proof of the&lt;/span&gt;&lt;span style=&quot;left:183.208px;top:792.462px;16.6043px;sans-serif;transform:scaleX(0.999485);&quot;&gt; agglomeration conjecture by Chiquet et al. (2017). Because we believe this theorem has &lt;/span&gt;&lt;span style=&quot;left:183.208px;top:812.388px;16.6043px;sans-serif;transform:scaleX(0.992218);&quot;&gt;independent interest, we restate and reprove the Chiquet et al. (2017) result herein.&lt;/span&gt;</style></abstract><issue><style face="normal" font="default" size="100%">225</style></issue><notes><style face="normal" font="default" size="100%">Arxiv link: &lt;a href=&quot;http://arxiv.org/abs/1902.07137&quot;&gt;http://arxiv.org/abs/1902.07137&lt;/a&gt;</style></notes></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Vavasis, Stephen</style></author><author><style face="normal" font="default" size="100%">Papoulia, Katerina</style></author><author><style face="normal" font="default" size="100%">Hirmand, M. Reza</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Second-order cone interior-point method for quasistatic and moderate dynamic cohesive fracture</style></title><secondary-title><style face="normal" font="default" size="100%">Comput. Meth. Appl.  Mech. Engr.</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2020</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://arxiv.org/abs/1909.10641</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">358</style></volume><pages><style face="normal" font="default" size="100%">112633</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;
	Second-order cone interior-point method for quasistatic and moderate dynamic cohesive fracture by S. Vavasis, &lt;a href=&quot;https://www.tesseraesolutions.com&quot;&gt;K. Papoulia&lt;/a&gt;, M. R. Hirmand
&lt;/p&gt;

&lt;p&gt;
	&amp;nbsp; Cohesive fracture is among the few techniques able to&lt;br&gt;&amp;nbsp; model complex fracture nucleation and propagation&lt;br&gt;&amp;nbsp; with a sharp (nonsmeared) representation&lt;br&gt;&amp;nbsp; of the crack.&amp;nbsp; Implicit time-stepping schemes are often favored&lt;br&gt;&amp;nbsp; in mechanics due to their ability to take larger time steps in&lt;br&gt;&amp;nbsp; quasistatic and moderate dynamic problems.&amp;nbsp; Furthermore,&lt;br&gt;&amp;nbsp; initially rigid cohesive models are typically preferred when&lt;br&gt;&amp;nbsp; the location of the crack is not known in advance, since&lt;br&gt;&amp;nbsp; initially elastic models artificially lower the material stiffness.&lt;br&gt;&amp;nbsp; It is challenging to include an initially rigid&lt;br&gt;&amp;nbsp; cohesive model in an implicit scheme because&lt;br&gt;&amp;nbsp; the initiation of fracture corresponds&lt;br&gt;&amp;nbsp; to a nondifferentiability of the underlying potential.&amp;nbsp; In&lt;br&gt;&amp;nbsp; this work, an interior-point method is proposed for implicit time&lt;br&gt;&amp;nbsp; stepping of initially rigid cohesive&lt;br&gt;&amp;nbsp; fracture.&amp;nbsp; It uses techniques developed for convex second-order&lt;br&gt;&amp;nbsp; cone programming for the nonconvex problem at hand.&amp;nbsp; The underlying cohesive model&lt;br&gt;&amp;nbsp; is taken from Papoulia (2017) and is based on a nondifferentiable&lt;br&gt;&amp;nbsp; energy function.&amp;nbsp; That previous work proposed an algorithm based on successive&lt;br&gt;&amp;nbsp; smooth approximations to the nondifferential objective for solving&lt;br&gt;&amp;nbsp; the resulting optimization problem.&amp;nbsp; It is argued herein that cone&lt;br&gt;&amp;nbsp; programming can capture the nondifferentiability without smoothing,&lt;br&gt;&amp;nbsp; and the resulting cone formulation is amenable to interior-point&lt;br&gt;&amp;nbsp; algorithms.&amp;nbsp; A further benefit of the formulation is that other&lt;br&gt;&amp;nbsp; conic inequality constraints are straightforward to incorporate.&lt;br&gt;&amp;nbsp; Computational results are provided showing that certain contact&lt;br&gt;&amp;nbsp; constraints can be easily handled and that the&lt;br&gt;&amp;nbsp; method is practical.
&lt;/p&gt;

&lt;p&gt;
	&amp;nbsp;
&lt;/p&gt;
</style></abstract><notes><style face="normal" font="default" size="100%">Arxiv version: &lt;a href=&quot;https://arxiv.org/abs/1909.10641&quot;&gt;https://arxiv.org/abs/1909.10641&lt;/a&gt;</style></notes></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>36</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Sina Baghal</style></author><author><style face="normal" font="default" size="100%">Courtney Paquette</style></author><author><style face="normal" font="default" size="100%">Stephen Vavasis</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">A termination criterion for stochastic gradient descent for binary classification</style></title></titles><dates><year><style  face="normal" font="default" size="100%">2020</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://arxiv.org/abs/2003.10312</style></url></web-urls></urls><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;span style=&quot;left:184.599px;top:355.992px;14.944px;sans-serif;transform:scaleX(1.0592);&quot;&gt;We propose a new, simple, and computationally inexpensive t&lt;/span&gt;&lt;span style=&quot;left:606.199px;top:355.992px;14.944px;sans-serif;transform:scaleX(1.04647);&quot;&gt;ermination test for constant step-size&lt;/span&gt;&lt;span style=&quot;left:161.599px;top:374.192px;14.944px;sans-serif;transform:scaleX(0.993215);&quot;&gt;stochastic gradient descent (SGD) applied to binary classi&lt;/span&gt;&lt;span style=&quot;left:562.799px;top:374.192px;14.944px;sans-serif;transform:scaleX(1.00203);&quot;&gt;fication on the logistic and hinge loss with &lt;/span&gt;&lt;span style=&quot;left:161.599px;top:392.392px;14.944px;sans-serif;transform:scaleX(1.01251);&quot;&gt;homogeneous linear predictors. Our theoretical results su&lt;/span&gt;&lt;span style=&quot;left:543.399px;top:392.392px;14.944px;sans-serif;transform:scaleX(1.03895);&quot;&gt;pport the effectiveness of our stopping criterion&lt;/span&gt;&lt;span style=&quot;left:161.599px;top:410.792px;14.944px;sans-serif;transform:scaleX(1.03051);&quot;&gt; when the data is Gaussian distributed. This presence of nois&lt;/span&gt;&lt;span style=&quot;left:568.599px;top:410.792px;14.944px;sans-serif;transform:scaleX(1.04244);&quot;&gt;e allows for the possibility of non-separable &lt;/span&gt;&lt;span style=&quot;left:161.599px;top:428.992px;14.944px;sans-serif;transform:scaleX(1.04835);&quot;&gt;data. We show that our test terminates in a finite number of ite&lt;/span&gt;&lt;span style=&quot;left:587.199px;top:428.992px;14.944px;sans-serif;transform:scaleX(1.04307);&quot;&gt;rations and when the noise in the data is&lt;/span&gt;&lt;span style=&quot;left:161.599px;top:447.192px;14.944px;sans-serif;transform:scaleX(1.05408);&quot;&gt;not too large, the expected classifier at termination nearly &lt;/span&gt;&lt;span style=&quot;left:554.199px;top:447.192px;14.944px;sans-serif;transform:scaleX(1.03973);&quot;&gt;minimizes the probability of misclassification.&lt;/span&gt;&lt;span style=&quot;left:161.599px;top:465.592px;14.944px;sans-serif;transform:scaleX(1.07723);&quot;&gt; Finally, numerical experiments indicate for both real and s&lt;/span&gt;&lt;span style=&quot;left:561.199px;top:465.592px;14.944px;sans-serif;transform:scaleX(1.09668);&quot;&gt;ynthetic data sets that our termination test &lt;/span&gt;&lt;span style=&quot;left:161.599px;top:483.792px;14.944px;sans-serif;transform:scaleX(1.05984);&quot;&gt;exhibits a good degree of predictability on accuracy and run&lt;/span&gt;&lt;span style=&quot;left:567.599px;top:483.792px;14.944px;sans-serif;transform:scaleX(1.07936);&quot;&gt;ning time.&lt;/span&gt;</style></abstract></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>5</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Doan, X. V.</style></author><author><style face="normal" font="default" size="100%">Vavasis, S.</style></author></authors><secondary-authors><author><style face="normal" font="default" size="100%">Le Thi et al.</style></author></secondary-authors></contributors><titles><title><style face="normal" font="default" size="100%">Low-rank matrix recovery with Ky Fan 2-k-norm</style></title><secondary-title><style face="normal" font="default" size="100%">Optimization of Complex Systems: Theory, Models and Applications</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2019</style></year></dates><pages><style face="normal" font="default" size="100%">310-319</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><notes><style face="normal" font="default" size="100%">Arxiv link: &lt;a href=&quot;https://arxiv.org/abs/1904.05590&quot;&gt;https://arxiv.org/abs/1904.05590&lt;/a&gt;</style></notes></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>34</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Paquette, C.</style></author><author><style face="normal" font="default" size="100%">Vavasis, S.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Potential-based analyses of first-order methods for constrained and composite optimization</style></title></titles><dates><year><style  face="normal" font="default" size="100%">2019</style></year></dates><language><style face="normal" font="default" size="100%">eng</style></language><notes><style face="normal" font="default" size="100%">Arxiv link: &lt;a href=&quot;http://arxiv.org/abs/1903.08497&quot;&gt;http://arxiv.org/abs/1903.08497&lt;/a&gt;</style></notes></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Nicolas Gillis</style></author><author><style face="normal" font="default" size="100%">Stephen A. Vavasis</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">On the Complexity of Robust PCA and l1-Norm Low-Rank Matrix Approximation</style></title><secondary-title><style face="normal" font="default" size="100%">Mathematics of Operations Research</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2018</style></year></dates><volume><style face="normal" font="default" size="100%">43</style></volume><pages><style face="normal" font="default" size="100%">1072-1084</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><notes><style face="normal" font="default" size="100%">Arxiv link: &lt;a href=&quot;https://arxiv.org/abs/1509.09236&quot;&gt;https://arxiv.org/abs/1509.09236&lt;/a&gt;</style></notes></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>34</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">S. Vavasis</style></author><author><style face="normal" font="default" size="100%">K. Papoulia</style></author><author><style face="normal" font="default" size="100%">M. Hirmand</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Second-order cone interior-point method for quasistatic and moderate dynamic cohesive fracture</style></title></titles><dates><year><style  face="normal" font="default" size="100%">2018</style></year></dates><language><style face="normal" font="default" size="100%">eng</style></language><notes><style face="normal" font="default" size="100%">submitted for publication, CMAME</style></notes></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">S. Karimi</style></author><author><style face="normal" font="default" size="100%">S. Vavasis</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">IMRO: A Proximal Quasi-Newton Method for Solving $\ell_1$-Regularized Least Squares Problems</style></title><secondary-title><style face="normal" font="default" size="100%">SIAM J. Optimiz</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2017</style></year></dates><volume><style face="normal" font="default" size="100%">27</style></volume><pages><style face="normal" font="default" size="100%">583-615</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><notes><style face="normal" font="default" size="100%">Arxiv link: &lt;a href=&quot;https://arxiv.org/abs/1401.4220&quot;&gt;https://arxiv.org/abs/1401.4220&lt;/a&gt;</style></notes></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>34</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Sahar Karimi</style></author><author><style face="normal" font="default" size="100%">Stephen Vavasis</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">A single potential governing convergence of conjugate gradient, accelerated gradient and geometric descent</style></title></titles><dates><year><style  face="normal" font="default" size="100%">2017</style></year></dates><language><style face="normal" font="default" size="100%">eng</style></language><notes><style face="normal" font="default" size="100%">Arxiv link: &lt;a href=&quot;https://arxiv.org/abs/1712.09498&quot;&gt;https://arxiv.org/abs/1712.09498&lt;/a&gt;</style></notes></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">X. V. Doan</style></author><author><style face="normal" font="default" size="100%">S. Vavasis</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Finding the largest low-rank clusters with Ky Fan 2-k-norm and l1-norm</style></title><secondary-title><style face="normal" font="default" size="100%">SIAM J. Optim.</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2016</style></year></dates><volume><style face="normal" font="default" size="100%">26</style></volume><pages><style face="normal" font="default" size="100%">274-312</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><notes><style face="normal" font="default" size="100%">Arxiv link: &lt;a href=&quot;https://arxiv.org/abs/1403.5901&quot;&gt;https://arxiv.org/abs/1403.5901&lt;/a&gt;</style></notes></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>34</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">S. Karimi</style></author><author><style face="normal" font="default" size="100%">S. Vavasis</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">A unified convergence bound for conjugate gradient and accelerated gradient</style></title></titles><dates><year><style  face="normal" font="default" size="100%">2016</style></year></dates><language><style face="normal" font="default" size="100%">eng</style></language><notes><style face="normal" font="default" size="100%">Arxiv link: &lt;a href=&quot;http://arxiv.org/abs/1605.00320&quot;&gt;http://arxiv.org/abs/1605.00320&lt;/a&gt;</style></notes></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Drusvyatskiy, D.</style></author><author><style face="normal" font="default" size="100%">Vavasis, S. A.</style></author><author><style face="normal" font="default" size="100%">Wolkowicz, H.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Extreme point inequalities and geometry of the rank sparsity ball</style></title><secondary-title><style face="normal" font="default" size="100%">Mathematical Programming</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2015</style></year><pub-dates><date><style  face="normal" font="default" size="100%">Aug</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://doi.org/10.1007/s10107-014-0795-8</style></url></web-urls></urls><number><style face="normal" font="default" size="100%">1</style></number><volume><style face="normal" font="default" size="100%">152</style></volume><pages><style face="normal" font="default" size="100%">521–544</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">We investigate geometric features of the unit ball corresponding to the sum of the nuclear norm of a matrix and the \$\$l_1\$\$l1norm of its entries–-a common penalty function encouraging joint low rank and high sparsity. As a byproduct of this effort, we develop a calculus (or algebra) of faces for general convex functions, yielding a simple and unified approach for deriving inequalities balancing the various features of the optimization problem at hand, at the extreme points of the solution set.</style></abstract><notes><style face="normal" font="default" size="100%">Arxiv link: &lt;a href=&quot;https://arxiv.org/abs/1401.4774&quot;&gt;https://arxiv.org/abs/1401.4774&lt;/a&gt;</style></notes></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Nicolas Gillis</style></author><author><style face="normal" font="default" size="100%">Stephen A. Vavasis</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Semidefinite Programming Based Preconditioning for More Robust Near-Separable Nonnegative Matrix Factorization</style></title><secondary-title><style face="normal" font="default" size="100%">SIAM J. Optim.</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2015</style></year></dates><number><style face="normal" font="default" size="100%">1</style></number><volume><style face="normal" font="default" size="100%">25</style></volume><pages><style face="normal" font="default" size="100%">677-698</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><notes><style face="normal" font="default" size="100%">Arxiv link: &lt;a href=&quot;https://arxiv.org/abs/1310.2273&quot;&gt;https://arxiv.org/abs/1310.2273&lt;/a&gt;</style></notes></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Brendan P.W. Ames</style></author><author><style face="normal" font="default" size="100%">Stephen A. Vavasis</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Convex optimization for the planted k-disjoint-clique problem</style></title><secondary-title><style face="normal" font="default" size="100%">Math. Progr.</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2014</style></year></dates><volume><style face="normal" font="default" size="100%">143</style></volume><pages><style face="normal" font="default" size="100%">299-337</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><notes><style face="normal" font="default" size="100%">Arxiv link: &lt;a href=&quot;https://arxiv.org/abs/1008.2814&quot;&gt;https://arxiv.org/abs/1008.2814&lt;/a&gt;</style></notes></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>34</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">L. Elkin</style></author><author><style face="normal" font="default" size="100%">Ting Kei Pong</style></author><author><style face="normal" font="default" size="100%">S. Vavasis</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Convex relaxation for finding planted influential nodes in a social network</style></title></titles><dates><year><style  face="normal" font="default" size="100%">2013</style></year></dates><language><style face="normal" font="default" size="100%">eng</style></language><notes><style face="normal" font="default" size="100%">Arxiv link: &lt;a href=&quot;http://arxiv.org/abs/1307.4047&quot;&gt;http://arxiv.org/abs/1307.4047&lt;/a&gt;</style></notes></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">N. Gillis</style></author><author><style face="normal" font="default" size="100%">S. A. Vavasis</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Fast and Robust Recursive Algorithms for Separable Nonnegative Matrix Factorization</style></title><secondary-title><style face="normal" font="default" size="100%">IEEE Trans. Pattern Analysis and Machine Intelligence</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2013</style></year></dates><volume><style face="normal" font="default" size="100%">36</style></volume><pages><style face="normal" font="default" size="100%">698-714</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><notes><style face="normal" font="default" size="100%">Arxiv link: &lt;a href=&quot;https://arxiv.org/abs/1208.1237&quot;&gt;https://arxiv.org/abs/1208.1237&lt;/a&gt;</style></notes></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">X. V. Doan</style></author><author><style face="normal" font="default" size="100%">S. Vavasis</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Finding approximately rank-one submatrices with the nuclear norm and $\ell_1$ norm</style></title><secondary-title><style face="normal" font="default" size="100%">SIAM J. Optimiz.</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2013</style></year></dates><volume><style face="normal" font="default" size="100%">23</style></volume><pages><style face="normal" font="default" size="100%">2502-2540</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><notes><style face="normal" font="default" size="100%">Arxiv link: &lt;a href=&quot;https://arxiv.org/abs/1011.1839&quot;&gt;https://arxiv.org/abs/1011.1839&lt;/a&gt;</style></notes></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">X. V. Doan</style></author><author><style face="normal" font="default" size="100%">K.-C. Toh</style></author><author><style face="normal" font="default" size="100%">S. Vavasis</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">A proximal point algorithm for sequential feature extraction applications</style></title><secondary-title><style face="normal" font="default" size="100%">SIAM J. Sci. Comput.</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2013</style></year></dates><pages><style face="normal" font="default" size="100%">A517-A540</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><notes><style face="normal" font="default" size="100%">&lt;a href=&quot;https://arxiv.org/abs/1108.0986&quot;&gt;https://arxiv.org/abs/1108.0986&lt;/a&gt;</style></notes></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>34</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">S. Vavasis</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Some notes on applying computational divided differencing in optimization</style></title></titles><dates><year><style  face="normal" font="default" size="100%">2013</style></year></dates><language><style face="normal" font="default" size="100%">eng</style></language><notes><style face="normal" font="default" size="100%">Arxiv link: &lt;a href=&quot;http://arxiv.org/abs/1307.4097&quot;&gt;http://arxiv.org/abs/1307.4097&lt;/a&gt;</style></notes></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>34</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">S. Karimi</style></author><author><style face="normal" font="default" size="100%">S. Vavasis</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Detecting and correcting loss of independence in nonlinear conjugate gradient</style></title></titles><dates><year><style  face="normal" font="default" size="100%">2012</style></year></dates><language><style face="normal" font="default" size="100%">eng</style></language><notes><style face="normal" font="default" size="100%">Arxiv link: &lt;a href=&quot;http://arxiv.org/abs/1202.1479&quot;&gt;http://arxiv.org/abs/1202.1479&lt;/a&gt;</style></notes></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>47</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">S. Sastry</style></author><author><style face="normal" font="default" size="100%">S. Shontz</style></author><author><style face="normal" font="default" size="100%">S. Vavasis</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">A log-barrier method for mesh quality improvement</style></title><secondary-title><style face="normal" font="default" size="100%">Proceedings of 20th International Meshing Roundtable</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2012</style></year></dates><publisher><style face="normal" font="default" size="100%">Springer</style></publisher><pages><style face="normal" font="default" size="100%">329-346</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><notes><style face="normal" font="default" size="100%">&lt;a href=&quot;http://www.math.uwaterloo.ca/~vavasis/sastry_shontz_vavasis.pdf&quot;&gt;Preliminary  version&lt;/a&gt; appeared in Proceedings of the 2011 International Meshing Roundtable. </style></notes></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Gun Srijuntongsiri</style></author><author><style face="normal" font="default" size="100%">Stephen Vavasis</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">A condition number analysis of an algorithm for solving a system of polynomial equations with one degree of freedom</style></title><secondary-title><style face="normal" font="default" size="100%">SIAM J. Sci. Comput.</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2011</style></year></dates><volume><style face="normal" font="default" size="100%">33</style></volume><pages><style face="normal" font="default" size="100%">433-454</style></pages><language><style face="normal" font="default" size="100%">eng</style></language></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Ames, B.</style></author><author><style face="normal" font="default" size="100%">Vavasis, S.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Nuclear norm minimization for the planted clique and biclique problems</style></title><secondary-title><style face="normal" font="default" size="100%">Mathematical Programming</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2011</style></year></dates><number><style face="normal" font="default" size="100%">1</style></number><volume><style face="normal" font="default" size="100%">129</style></volume><pages><style face="normal" font="default" size="100%">69-89</style></pages><language><style face="normal" font="default" size="100%">eng</style></language></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">S. Shontz</style></author><author><style face="normal" font="default" size="100%">S. Vavasis</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">A robust solution procedure for hyperelastic solids with large boundary deformation</style></title><secondary-title><style face="normal" font="default" size="100%">\em Engineering with Computers</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2011</style></year></dates><number><style face="normal" font="default" size="100%">2</style></number><volume><style face="normal" font="default" size="100%">28</style></volume><pages><style face="normal" font="default" size="100%">135-147</style></pages><language><style face="normal" font="default" size="100%">eng</style></language></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">S. Shontz</style></author><author><style face="normal" font="default" size="100%">S. Vavasis</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Analysis of and workarounds for element reversal for a finite element-based algorithm for warping triangular and tetrahedral meshes</style></title><secondary-title><style face="normal" font="default" size="100%">BIT Numerical Mathematics</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2010</style></year></dates><number><style face="normal" font="default" size="100%">4</style></number><volume><style face="normal" font="default" size="100%">50</style></volume><pages><style face="normal" font="default" size="100%">863-884</style></pages><language><style face="normal" font="default" size="100%">eng</style></language></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Stephen A. Vavasis</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">On the complexity of nonnegative matrix factorization</style></title><secondary-title><style face="normal" font="default" size="100%">SIAM J. Optim.</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2009</style></year></dates><number><style face="normal" font="default" size="100%">3</style></number><volume><style face="normal" font="default" size="100%">20</style></volume><pages><style face="normal" font="default" size="100%">1364-1377</style></pages><language><style face="normal" font="default" size="100%">eng</style></language></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Gun Srijuntongsiri</style></author><author><style face="normal" font="default" size="100%">Stephen A. Vavasis</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">A Condition Number Analysis of a Line-Surface Intersection Algorithm</style></title><secondary-title><style face="normal" font="default" size="100%">SIAM J. Sci. Comput.</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2008</style></year></dates><volume><style face="normal" font="default" size="100%">30</style></volume><pages><style face="normal" font="default" size="100%">1064-1081</style></pages><language><style face="normal" font="default" size="100%">eng</style></language></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>34</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Stephen A. Vavasis</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">A new secant method for unconstrained optimization</style></title></titles><dates><year><style  face="normal" font="default" size="100%">2008</style></year></dates><language><style face="normal" font="default" size="100%">eng</style></language><notes><style face="normal" font="default" size="100%">Archived in arxiv.org, 0808.2316</style></notes></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>47</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Michael Biggs</style></author><author><style face="normal" font="default" size="100%">Ali Ghodsi</style></author><author><style face="normal" font="default" size="100%">Stephen A. Vavasis</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Nonnegative matrix factorization via rank-one downdating</style></title><secondary-title><style face="normal" font="default" size="100%">Proceedings of the 2008 International Conference on Machine Learning</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2008</style></year></dates><language><style face="normal" font="default" size="100%">eng</style></language><notes><style face="normal" font="default" size="100%">Proceedings published online at \urlhttp://icml2008.cs.helsinki.fi/abstracts.shtml, Preliminary version of the full paper in arxiv.org, 0808.0120</style></notes></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">E. Boman</style></author><author><style face="normal" font="default" size="100%">B. Hendrickson</style></author><author><style face="normal" font="default" size="100%">S. Vavasis</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Solving Elliptic Finite Element Systems in Near-Linear Time with Support Preconditioners</style></title><secondary-title><style face="normal" font="default" size="100%">SIAM J. Numer. Anal.</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2008</style></year></dates><volume><style face="normal" font="default" size="100%">46</style></volume><pages><style face="normal" font="default" size="100%">3264-3284</style></pages><language><style face="normal" font="default" size="100%">eng</style></language></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>34</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Gun Srijuntongsiri</style></author><author><style face="normal" font="default" size="100%">Stephen A. Vavasis</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">A Condition Number Analysis of a Surface-Surface Intersection Algorithm</style></title></titles><dates><year><style  face="normal" font="default" size="100%">2007</style></year></dates><language><style face="normal" font="default" size="100%">eng</style></language><notes><style face="normal" font="default" size="100%">Archived in arxiv.org, 0711.4656</style></notes></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>34</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Gun Srijuntongsiri</style></author><author><style face="normal" font="default" size="100%">Stephen A. Vavasis</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Properties of polynomial bases used in line-surface intersection algorithm</style></title></titles><dates><year><style  face="normal" font="default" size="100%">2007</style></year></dates><language><style face="normal" font="default" size="100%">eng</style></language><notes><style face="normal" font="default" size="100%">Archived in arxiv.org, 0707.1515; submitted to ICCEE 2008 Conference</style></notes></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">P. Ganguly</style></author><author><style face="normal" font="default" size="100%">S. Vavasis</style></author><author><style face="normal" font="default" size="100%">K. Papoulia</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">An algorithm for two-dimensional mesh generation based on the pinwheel tiling</style></title><secondary-title><style face="normal" font="default" size="100%">SIAM J. Scientific Computing</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2006</style></year></dates><volume><style face="normal" font="default" size="100%">28</style></volume><pages><style face="normal" font="default" size="100%">1533-1562</style></pages><language><style face="normal" font="default" size="100%">eng</style></language></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>34</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">S. Vavasis</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">A conjecture that the roots of a univariate polynomial lie in a union of annuli</style></title></titles><dates><year><style  face="normal" font="default" size="100%">2006</style></year></dates><language><style face="normal" font="default" size="100%">eng</style></language><notes><style face="normal" font="default" size="100%">Archived in arxiv.org, math.CV/0606194</style></notes></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">K. Papoulia</style></author><author><style face="normal" font="default" size="100%">S. Vavasis</style></author><author><style face="normal" font="default" size="100%">P. Ganguly</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Spatial convergence of crack nucleation using a cohesive finite element model on a pinwheel-based mesh</style></title><secondary-title><style face="normal" font="default" size="100%">Internat. J. Numer. Meth. Eng.</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2006</style></year></dates><volume><style face="normal" font="default" size="100%">67</style></volume><pages><style face="normal" font="default" size="100%">1-16</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;
Spatial convergence of crack nucleation using a cohesive finite‐element model on a pinwheel‐based mesh by 
&lt;a href=&quot;https://tesseraesolutions.com&quot;&gt;Katerina D. Papoulia&lt;/a&gt;,
Stephen A. Vavasis,
Pritam Ganguly
&lt;/p&gt;

&lt;p&gt;
We consider the use of initially rigid cohesive interface models in a two‐dimensional dynamic finite‐element solution of a fracture process. Our focus is on convergence of finite‐element solutions to a solution of the undiscretized medium as the mesh spacing Δ&lt;i&gt;x&lt;/i&gt; (and therefore time‐step Δ&lt;i&gt;t&lt;/i&gt;) tends to zero. We propose the use of pinwheel meshes, which possess the ‘isoperimetric property’ that for any curve &lt;i&gt;C&lt;/i&gt; in the computational domain, there is an approximation to &lt;i&gt;C&lt;/i&gt; using mesh edges that tends to &lt;i&gt;C&lt;/i&gt; including a correct representation of its length, as the grid size tends to zero. We suggest that the isoperimetric property is a necessary condition for any possible spatial convergence proof in the general case that the crack path is not known in advance. Conversely, we establish that if the pinwheel mesh is used, the discrete interface first activated in the finite‐element model will converge to the initial crack in the undiscretized medium. Finally, we carry out a mesh refinement experiment to check convergence of both nucleation and propagation. Our results indicate that the crack path computed in the pinwheel mesh is more stable as the mesh is refined compared to other types of meshes.</style></abstract></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">G. Jónsson</style></author><author><style face="normal" font="default" size="100%">S. Vavasis</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Accurate solution of polynomial equations using Macaulay resultant matrices</style></title><secondary-title><style face="normal" font="default" size="100%">Mathematics of Computation</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2005</style></year></dates><volume><style face="normal" font="default" size="100%">74</style></volume><pages><style face="normal" font="default" size="100%">221-262</style></pages><language><style face="normal" font="default" size="100%">eng</style></language></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">V. E. Howle</style></author><author><style face="normal" font="default" size="100%">S. A. Vavasis</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">An iterative method for solving complex-symmetric systems arising in electrical power modeling</style></title><secondary-title><style face="normal" font="default" size="100%">SIAM J. Matrix Analysis App.</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2005</style></year></dates><volume><style face="normal" font="default" size="100%">26</style></volume><pages><style face="normal" font="default" size="100%">1150-1178</style></pages><language><style face="normal" font="default" size="100%">eng</style></language></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Chin-Hang Sam</style></author><author><style face="normal" font="default" size="100%">K. Papoulia</style></author><author><style face="normal" font="default" size="100%">S. Vavasis</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Obtaining initially rigid cohesive finite element models that are temporally convergent</style></title><secondary-title><style face="normal" font="default" size="100%">Engineering Fracture Mechanics</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2005</style></year></dates><volume><style face="normal" font="default" size="100%">72</style></volume><pages><style face="normal" font="default" size="100%">2247-2267</style></pages><language><style face="normal" font="default" size="100%">eng</style></language></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">G. Jónsson</style></author><author><style face="normal" font="default" size="100%">S. Vavasis</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Solving polynomials with small leading coefficients</style></title><secondary-title><style face="normal" font="default" size="100%">SIAM J. Matrix Analysis App.</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2005</style></year></dates><volume><style face="normal" font="default" size="100%">26</style></volume><pages><style face="normal" font="default" size="100%">400-414</style></pages><language><style face="normal" font="default" size="100%">eng</style></language></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>34</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Gun Srijuntongsiri</style></author><author><style face="normal" font="default" size="100%">S. Vavasis</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">A Fully Sparse Implementation of a Primal- Dual Interior-Point Potential Reduction Method for Semidefinite Programming</style></title></titles><dates><year><style  face="normal" font="default" size="100%">2004</style></year></dates><language><style face="normal" font="default" size="100%">eng</style></language><notes><style face="normal" font="default" size="100%">Archived in arxiv.org, cs.NA/0412009</style></notes></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>34</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">S. Vavasis</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">A Bernstein-Bézier Sufficient Condition for Invertibility of Polynomial Mappings</style></title></titles><dates><year><style  face="normal" font="default" size="100%">2003</style></year></dates><language><style face="normal" font="default" size="100%">eng</style></language><notes><style face="normal" font="default" size="100%">Archived by arxiv.org, cs.NA/0308021</style></notes></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">K. Papoulia</style></author><author><style face="normal" font="default" size="100%">S. Vavasis</style></author><author><style face="normal" font="default" size="100%">C.-H. Sam</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Time continuity in cohesive finite element modeling</style></title><secondary-title><style face="normal" font="default" size="100%">International J. Numer. Meth. Eng.</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2003</style></year></dates><number><style face="normal" font="default" size="100%">5</style></number><volume><style face="normal" font="default" size="100%">58</style></volume><pages><style face="normal" font="default" size="100%">679-701</style></pages><language><style face="normal" font="default" size="100%">eng</style></language></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">E. Y. Bobrovnikova</style></author><author><style face="normal" font="default" size="100%">S. A. Vavasis</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Accurate Solution of Weighted Least Squares by Iterative Methods</style></title><secondary-title><style face="normal" font="default" size="100%">SIAM J. Matrix Anal. App.</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2001</style></year></dates><volume><style face="normal" font="default" size="100%">22</style></volume><pages><style face="normal" font="default" size="100%">1153-1174</style></pages><language><style face="normal" font="default" size="100%">eng</style></language></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">E. Bobrovnikova</style></author><author><style face="normal" font="default" size="100%">S. Vavasis</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">A Norm Bound for Projections with Complex Weights</style></title><secondary-title><style face="normal" font="default" size="100%">Linear Algebra and its Applications</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2000</style></year></dates><volume><style face="normal" font="default" size="100%">307</style></volume><pages><style face="normal" font="default" size="100%">69-75</style></pages><language><style face="normal" font="default" size="100%">eng</style></language></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">S. A. Mitchell</style></author><author><style face="normal" font="default" size="100%">S. A. Vavasis</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Quality Mesh Generation in Higher Dimensions</style></title><secondary-title><style face="normal" font="default" size="100%">SIAM J. Computing</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2000</style></year></dates><volume><style face="normal" font="default" size="100%">29</style></volume><pages><style face="normal" font="default" size="100%">1334-1370</style></pages><language><style face="normal" font="default" size="100%">eng</style></language></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>5</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">S. A. Vavasis</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Convex Optimization</style></title><secondary-title><style face="normal" font="default" size="100%">Algorithms and Theory of Computation Handbook</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">1999</style></year></dates><publisher><style face="normal" font="default" size="100%">CRC Press</style></publisher><language><style face="normal" font="default" size="100%">eng</style></language></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>34</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">S. Vavasis</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">A note on efficient computation of the gradient in semidefinite programming</style></title></titles><dates><year><style  face="normal" font="default" size="100%">1999</style></year></dates><language><style face="normal" font="default" size="100%">eng</style></language><notes><style face="normal" font="default" size="100%">Preprint</style></notes></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">G. L. Miller</style></author><author><style face="normal" font="default" size="100%">S.-H. Teng</style></author><author><style face="normal" font="default" size="100%">W. Thurston</style></author><author><style face="normal" font="default" size="100%">S. Vavasis</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Geometric Separators for Finite-Element Meshes</style></title><secondary-title><style face="normal" font="default" size="100%">SIAM J. Sci. Comput.</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">1998</style></year></dates><volume><style face="normal" font="default" size="100%">19</style></volume><pages><style face="normal" font="default" size="100%">364-386</style></pages><language><style face="normal" font="default" size="100%">eng</style></language></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">T. A. Driscoll</style></author><author><style face="normal" font="default" size="100%">S. A. Vavasis</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Numerical conformal mapping using cross-ratios and Delaunay triangulation</style></title><secondary-title><style face="normal" font="default" size="100%">SIAM J. Sci. Comput.</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">1998</style></year></dates><volume><style face="normal" font="default" size="100%">19</style></volume><pages><style face="normal" font="default" size="100%">1783-1803</style></pages><language><style face="normal" font="default" size="100%">eng</style></language></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>47</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">V. E. Howle</style></author><author><style face="normal" font="default" size="100%">S. Vavasis</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Preconditioning complex-symmetric layered systems arising in electrical power modeling</style></title><secondary-title><style face="normal" font="default" size="100%">Proceedings of the Copper Mountain Conference on Iterative Methods</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">1998</style></year></dates><language><style face="normal" font="default" size="100%">eng</style></language></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">P. Hough</style></author><author><style face="normal" font="default" size="100%">S. Vavasis</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Complete orthogonal decomposition for weighted least squares</style></title><secondary-title><style face="normal" font="default" size="100%">SIAM J. Matrix Anal. Appl.</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">1997</style></year></dates><volume><style face="normal" font="default" size="100%">18</style></volume><language><style face="normal" font="default" size="100%">eng</style></language></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">G. L. Miller</style></author><author><style face="normal" font="default" size="100%">S.-H. Teng</style></author><author><style face="normal" font="default" size="100%">W. Thurston</style></author><author><style face="normal" font="default" size="100%">S. A. Vavasis</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Separators for sphere-packings and nearest neighbor graphs</style></title><secondary-title><style face="normal" font="default" size="100%">J. ACM</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">1997</style></year></dates><volume><style face="normal" font="default" size="100%">44</style></volume><pages><style face="normal" font="default" size="100%">1-29</style></pages><language><style face="normal" font="default" size="100%">eng</style></language></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>47</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">S. A. Mitchell</style></author><author><style face="normal" font="default" size="100%">S. Vavasis</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">An aspect ratio bound for triangulating a $d$-grid cut by a hyperplane (extended abstract)</style></title><secondary-title><style face="normal" font="default" size="100%">Proc. 12th ACM Symposium on Computational Geometry</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">1996</style></year></dates><pages><style face="normal" font="default" size="100%">48-57</style></pages><language><style face="normal" font="default" size="100%">eng</style></language></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">S. A. Vavasis</style></author><author><style face="normal" font="default" size="100%">Y. Ye</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Identifying an Optimal Basis in Linear Programming</style></title><secondary-title><style face="normal" font="default" size="100%">Annals of Operations Research</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">1996</style></year></dates><volume><style face="normal" font="default" size="100%">62</style></volume><pages><style face="normal" font="default" size="100%">565–572</style></pages><language><style face="normal" font="default" size="100%">eng</style></language></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">S. A. Vavasis</style></author><author><style face="normal" font="default" size="100%">Y. Ye</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">A primal-dual interior point method whose running time depends only on the constraint matrix</style></title><secondary-title><style face="normal" font="default" size="100%">Mathematical Programming</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">1996</style></year></dates><volume><style face="normal" font="default" size="100%">74</style></volume><pages><style face="normal" font="default" size="100%">79–120</style></pages><language><style face="normal" font="default" size="100%">eng</style></language></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>34</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">S. A. Vavasis</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">QMG: Software for finite-element mesh generation</style></title></titles><dates><year><style  face="normal" font="default" size="100%">1996</style></year></dates><language><style face="normal" font="default" size="100%">eng</style></language><notes><style face="normal" font="default" size="100%">See \urlhttp://www.cs.cornell.edu/home/vavasis/qmg-home.html</style></notes></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>5</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">S. A. Vavasis</style></author><author><style face="normal" font="default" size="100%">Y. Ye</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">On the relationship between layered least squares and affine scaling steps</style></title><secondary-title><style face="normal" font="default" size="100%">Lectures in Applied Mathematics, volume 32</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">1996</style></year></dates><publisher><style face="normal" font="default" size="100%">American Mathematical Society</style></publisher><pub-location><style face="normal" font="default" size="100%">Providence, RI</style></pub-location><language><style face="normal" font="default" size="100%">eng</style></language></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">S. A. Vavasis</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Stable finite elements for problems with wild coefficients</style></title><secondary-title><style face="normal" font="default" size="100%">SIAM J. Numer. Anal.</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">1996</style></year></dates><volume><style face="normal" font="default" size="100%">33</style></volume><pages><style face="normal" font="default" size="100%">890–916</style></pages><language><style face="normal" font="default" size="100%">eng</style></language></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">S. A. Vavasis</style></author><author><style face="normal" font="default" size="100%">Y. Ye</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Condition Numbers for Polyhedra with Real Number Data</style></title><secondary-title><style face="normal" font="default" size="100%">Operations Research Letters</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">1995</style></year></dates><volume><style face="normal" font="default" size="100%">17</style></volume><pages><style face="normal" font="default" size="100%">209-214</style></pages><language><style face="normal" font="default" size="100%">eng</style></language></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>47</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">S. A. Vavasis</style></author><author><style face="normal" font="default" size="100%">Y. Ye</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">An accelerated interior point method whose running time depends only on $A$ (extended abstract)</style></title><secondary-title><style face="normal" font="default" size="100%">Proceedings of the 26th Symposium on the Theory of Computing</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">1994</style></year></dates><publisher><style face="normal" font="default" size="100%">ACM Press</style></publisher><pages><style face="normal" font="default" size="100%">512–521</style></pages><language><style face="normal" font="default" size="100%">eng</style></language></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>13</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">D. M. Bond</style></author><author><style face="normal" font="default" size="100%">S. A. Vavasis</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Fast Wavelet Transforms for Matrices Arising from Boundary Element Methods</style></title></titles><dates><year><style  face="normal" font="default" size="100%">1994</style></year></dates><number><style face="normal" font="default" size="100%">CTC94TR174</style></number><publisher><style face="normal" font="default" size="100%">Cornell Theory Center, Cornell University</style></publisher><language><style face="normal" font="default" size="100%">eng</style></language></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">S. A. Vavasis</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Stable numerical algorithms for equilibrium systems</style></title><secondary-title><style face="normal" font="default" size="100%">SIAM J. Matrix Anal. Appl</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">1994</style></year></dates><volume><style face="normal" font="default" size="100%">15</style></volume><pages><style face="normal" font="default" size="100%">1108–1131</style></pages><language><style face="normal" font="default" size="100%">eng</style></language></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">J. M. Stern</style></author><author><style face="normal" font="default" size="100%">S. A. Vavasis</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Active set methods for problems in column block angular form</style></title><secondary-title><style face="normal" font="default" size="100%">Matemática Aplicada e Computacional</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">1993</style></year></dates><volume><style face="normal" font="default" size="100%">12</style></volume><pages><style face="normal" font="default" size="100%">199–226</style></pages><language><style face="normal" font="default" size="100%">eng</style></language></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>5</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">G. Miller</style></author><author><style face="normal" font="default" size="100%">S.-H. Teng</style></author><author><style face="normal" font="default" size="100%">W. Thurston</style></author><author><style face="normal" font="default" size="100%">S. Vavasis</style></author></authors><secondary-authors><author><style face="normal" font="default" size="100%">Alan George</style></author><author><style face="normal" font="default" size="100%">John Gilbert</style></author><author><style face="normal" font="default" size="100%">Joseph W. H. Liu</style></author></secondary-authors></contributors><titles><title><style face="normal" font="default" size="100%">Automatic Mesh Partitioning</style></title><secondary-title><style face="normal" font="default" size="100%">Graph Theory and Sparse Matrix Computation</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">1993</style></year></dates><publisher><style face="normal" font="default" size="100%">Springer Verlag</style></publisher><language><style face="normal" font="default" size="100%">eng</style></language></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">S. A. Vavasis</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Black-box complexity of local minimization</style></title><secondary-title><style face="normal" font="default" size="100%">SIAM Journal on Optimization</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">1993</style></year></dates><volume><style face="normal" font="default" size="100%">3</style></volume><pages><style face="normal" font="default" size="100%">60–80</style></pages><language><style face="normal" font="default" size="100%">eng</style></language></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>5</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Vavasis, S. A.</style></author></authors><secondary-authors><author><style face="normal" font="default" size="100%">R. Horst</style></author><author><style face="normal" font="default" size="100%">P. M. Pardalos</style></author></secondary-authors></contributors><titles><title><style face="normal" font="default" size="100%">Complexity issues in global optimization: A survey</style></title><secondary-title><style face="normal" font="default" size="100%">Handbook for Global Optimization</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">1993</style></year></dates><publisher><style face="normal" font="default" size="100%">Kluwer Academic Publishers</style></publisher><language><style face="normal" font="default" size="100%">eng</style></language></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">J. M. Stern</style></author><author><style face="normal" font="default" size="100%">S. A. Vavasis</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Nested dissection for sparse nullspace bases</style></title><secondary-title><style face="normal" font="default" size="100%">simax</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">1993</style></year></dates><volume><style face="normal" font="default" size="100%">14</style></volume><pages><style face="normal" font="default" size="100%">766–775</style></pages><language><style face="normal" font="default" size="100%">eng</style></language></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>5</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Vavasis, S. A.</style></author></authors><secondary-authors><author><style face="normal" font="default" size="100%">P. M. Pardalos</style></author></secondary-authors></contributors><titles><title><style face="normal" font="default" size="100%">Polynomial time weak approximation algorithms for quadratic programming</style></title><secondary-title><style face="normal" font="default" size="100%">Complexity in Numerical Optimization</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">1993</style></year></dates><publisher><style face="normal" font="default" size="100%">World Scientific</style></publisher><pages><style face="normal" font="default" size="100%">490–500</style></pages><language><style face="normal" font="default" size="100%">eng</style></language></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>5</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Vavasis, S. A.</style></author></authors><secondary-authors><author><style face="normal" font="default" size="100%">C. A. Floudas</style></author><author><style face="normal" font="default" size="100%">P. M. Pardalos</style></author></secondary-authors></contributors><titles><title><style face="normal" font="default" size="100%">On approximation algorithms for concave quadratic programming</style></title><secondary-title><style face="normal" font="default" size="100%">Recent Advances in Global Optimization</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">1992</style></year></dates><publisher><style face="normal" font="default" size="100%">Princeton University Press</style></publisher><pub-location><style face="normal" font="default" size="100%">Princeton, N.J.</style></pub-location><pages><style face="normal" font="default" size="100%">3–18</style></pages><language><style face="normal" font="default" size="100%">eng</style></language></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Vavasis, S. A.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Approximation algorithms for indefinite quadratic programming</style></title></titles><dates><year><style  face="normal" font="default" size="100%">1992</style></year></dates><volume><style face="normal" font="default" size="100%">57</style></volume><pages><style face="normal" font="default" size="100%">279–311</style></pages><language><style face="normal" font="default" size="100%">eng</style></language></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">S. A. Vavasis</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Local minima for indefinite quadratic knapsack problems</style></title><secondary-title><style face="normal" font="default" size="100%">matpro</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">1992</style></year></dates><volume><style face="normal" font="default" size="100%">54</style></volume><pages><style face="normal" font="default" size="100%">127–153</style></pages><language><style face="normal" font="default" size="100%">eng</style></language></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>47</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">D. M. Bond</style></author><author><style face="normal" font="default" size="100%">S. A. Vavasis</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Multigrid for mixed boundary integral equations</style></title><secondary-title><style face="normal" font="default" size="100%">Proc. 1992 Copper Mountain Conference on Iterative Methods</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">1992</style></year></dates><language><style face="normal" font="default" size="100%">eng</style></language></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">S. A. Vavasis</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Preconditioners for boundary integral equations</style></title></titles><dates><year><style  face="normal" font="default" size="100%">1992</style></year></dates><volume><style face="normal" font="default" size="100%">13</style></volume><pages><style face="normal" font="default" size="100%">905–925</style></pages><language><style face="normal" font="default" size="100%">eng</style></language></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>47</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">S. A. Mitchell</style></author><author><style face="normal" font="default" size="100%">S. A. Vavasis</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Quality mesh generation in three dimensions</style></title><secondary-title><style face="normal" font="default" size="100%">Proceedings of the ACM Computational Geometry Conference</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">1992</style></year></dates><pages><style face="normal" font="default" size="100%">212–221</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><notes><style face="normal" font="default" size="100%">Also appeared as Cornell C.S. TR 92-1267</style></notes></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">S. A. Vavasis</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Automatic domain partitioning in three dimensions</style></title></titles><dates><year><style  face="normal" font="default" size="100%">1991</style></year></dates><volume><style face="normal" font="default" size="100%">12</style></volume><pages><style face="normal" font="default" size="100%">950–970</style></pages><language><style face="normal" font="default" size="100%">eng</style></language></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>13</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">H.-W. Hsu</style></author><author><style face="normal" font="default" size="100%">M. H. Lean</style></author><author><style face="normal" font="default" size="100%">P. L.-F. Liu</style></author><author><style face="normal" font="default" size="100%">S. A. Vavasis</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">A boundary element method for three-dimensional free surface flow</style></title></titles><dates><year><style  face="normal" font="default" size="100%">1991</style></year></dates><number><style face="normal" font="default" size="100%">X9100283</style></number><publisher><style face="normal" font="default" size="100%">Xerox</style></publisher><language><style face="normal" font="default" size="100%">eng</style></language></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>47</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">G. L. Miller</style></author><author><style face="normal" font="default" size="100%">S. A. Vavasis</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Density graphs and separators</style></title><secondary-title><style face="normal" font="default" size="100%">Proc. SIAM-ACM Symposium on Discrete Algorithms</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">1991</style></year></dates><language><style face="normal" font="default" size="100%">eng</style></language></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>6</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Vavasis, S. A.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Nonlinear Optimization: Complexity Issues</style></title></titles><dates><year><style  face="normal" font="default" size="100%">1991</style></year></dates><publisher><style face="normal" font="default" size="100%">Oxford University Press</style></publisher><pub-location><style face="normal" font="default" size="100%">New York</style></pub-location><language><style face="normal" font="default" size="100%">eng</style></language></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">P. M. Pardalos</style></author><author><style face="normal" font="default" size="100%">S. A. Vavasis</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Quadratic programming with one negative eigenvalue is NP-hard</style></title><secondary-title><style face="normal" font="default" size="100%">Journal of Global Optimization</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">1991</style></year></dates><volume><style face="normal" font="default" size="100%">1</style></volume><pages><style face="normal" font="default" size="100%">15–22</style></pages><language><style face="normal" font="default" size="100%">eng</style></language></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">J. J. Moré</style></author><author><style face="normal" font="default" size="100%">S. A. Vavasis</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">On the solution of concave knapsack problems</style></title><secondary-title><style face="normal" font="default" size="100%">matpro</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">1991</style></year></dates><volume><style face="normal" font="default" size="100%">49</style></volume><pages><style face="normal" font="default" size="100%">397–411</style></pages><language><style face="normal" font="default" size="100%">eng</style></language></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>47</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">G. L. Miller</style></author><author><style face="normal" font="default" size="100%">S.-H. Teng</style></author><author><style face="normal" font="default" size="100%">S. A. Vavasis</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">A unified geometric approach to graph separators</style></title><secondary-title><style face="normal" font="default" size="100%">Proceedings of the Symposium on Foundations of Computer Science</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">1991</style></year></dates><pages><style face="normal" font="default" size="100%">538–547</style></pages><language><style face="normal" font="default" size="100%">eng</style></language></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>13</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">S. A. Vavasis</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">A note on wavelet bases for two-dimensional surfaces</style></title></titles><dates><year><style  face="normal" font="default" size="100%">1990</style></year></dates><number><style face="normal" font="default" size="100%">90-1157</style></number><publisher><style face="normal" font="default" size="100%">Department of Computer Science, Cornell University</style></publisher><pub-location><style face="normal" font="default" size="100%">Ithaca, NY</style></pub-location><language><style face="normal" font="default" size="100%">eng</style></language></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>13</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Vavasis, S. A.</style></author><author><style face="normal" font="default" size="100%">Zippel, R.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Proving polynomial-time for sphere-constrained quadratic programming</style></title></titles><dates><year><style  face="normal" font="default" size="100%">1990</style></year></dates><number><style face="normal" font="default" size="100%">90-1182</style></number><publisher><style face="normal" font="default" size="100%">Department of Computer Science, Cornell University</style></publisher><pub-location><style face="normal" font="default" size="100%">Ithaca, NY</style></pub-location><language><style face="normal" font="default" size="100%">eng</style></language></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Vavasis, S. A.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Quadratic programming is in NP</style></title><secondary-title><style face="normal" font="default" size="100%">Information Processing Letters</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">1990</style></year></dates><volume><style face="normal" font="default" size="100%">36</style></volume><pages><style face="normal" font="default" size="100%">73–77</style></pages><language><style face="normal" font="default" size="100%">eng</style></language></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">M. D. Hirsch</style></author><author><style face="normal" font="default" size="100%">C. H. Papadimitriou</style></author><author><style face="normal" font="default" size="100%">S. A. Vavasis</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Exponential lower bounds for finding Brouwer fixed points</style></title><secondary-title><style face="normal" font="default" size="100%">Journal of Complexity</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">1989</style></year></dates><volume><style face="normal" font="default" size="100%">5</style></volume><pages><style face="normal" font="default" size="100%">379–416</style></pages><language><style face="normal" font="default" size="100%">eng</style></language></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">S. A. Vavasis</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Gaussian elimination with pivoting is P-complete</style></title><secondary-title><style face="normal" font="default" size="100%">SIAM Journal on Discrete Mathematics</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">1989</style></year></dates><volume><style face="normal" font="default" size="100%">2</style></volume><pages><style face="normal" font="default" size="100%">412–423</style></pages><language><style face="normal" font="default" size="100%">eng</style></language></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>47</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">M. D. Hirsch</style></author><author><style face="normal" font="default" size="100%">S. A. Vavasis</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Exponential lower bounds for finding Brouwer fixed points</style></title><secondary-title><style face="normal" font="default" size="100%">Proceedings 28th Symposium on Foundations of Computer Science</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">1987</style></year></dates><publisher><style face="normal" font="default" size="100%">IEEE Computer Society Press</style></publisher><pages><style face="normal" font="default" size="100%">401–-410</style></pages><language><style face="normal" font="default" size="100%">eng</style></language></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>5</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">K. J. Lieberherr</style></author><author><style face="normal" font="default" size="100%">S. A. Vavasis</style></author></authors><secondary-authors><author><style face="normal" font="default" size="100%">A. B. Cremers</style></author><author><style face="normal" font="default" size="100%">H. P. Kriegel</style></author></secondary-authors></contributors><titles><title><style face="normal" font="default" size="100%">Analysis of polynomial approximation algorithms for constraint expressions</style></title><secondary-title><style face="normal" font="default" size="100%">Theoretical Computer Science: 6th GI conference, Dortmund</style></secondary-title><tertiary-title><style face="normal" font="default" size="100%">Lecture Notes in Computer Science</style></tertiary-title></titles><dates><year><style  face="normal" font="default" size="100%">1982</style></year></dates><publisher><style face="normal" font="default" size="100%">Springer Verlag</style></publisher><pub-location><style face="normal" font="default" size="100%">Berlin</style></pub-location><volume><style face="normal" font="default" size="100%">145</style></volume><language><style face="normal" font="default" size="100%">eng</style></language></record></records></xml>