BEGIN:VCALENDAR VERSION:2.0 PRODID:-//Drupal iCal API//EN X-WR-CALNAME:Events items teaser X-WR-TIMEZONE:America/Toronto BEGIN:VTIMEZONE TZID:America/Toronto X-LIC-LOCATION:America/Toronto BEGIN:DAYLIGHT TZNAME:EDT TZOFFSETFROM:-0500 TZOFFSETTO:-0400 DTSTART:20260308T070000 END:DAYLIGHT BEGIN:STANDARD TZNAME:EST TZOFFSETFROM:-0400 TZOFFSETTO:-0500 DTSTART:20251102T060000 END:STANDARD END:VTIMEZONE BEGIN:VEVENT UID:6a7231a18d434 DTSTART;TZID=America/Toronto:20260807T100000 SEQUENCE:0 TRANSP:TRANSPARENT DTEND;TZID=America/Toronto:20260807T110000 URL:https://uwaterloo.ca/combinatorics-and-optimization/events/masters-thes is-presentation-ziwen-wang-solving-linear SUMMARY:Master's Thesis Presentation - ZiWen Wang - Solving Linear Programs \nwith very Tall Constraint Matrices CLASS:PUBLIC DESCRIPTION:SPEAKER: \n ZiWen Wang\n\nSUPERVISOR:\n Levent Tuncel\n\nLOCAT ION:\n MC 5479\n\nABSTRACT: \n\nGiven an LP with tall and skinny constrai nt matrix\, we will\nexploit this property and study an algorithm invent ed by Clarkson\n[8]. Although this algorithm has\nbeen around for over 30 years\, there were no software or\nimplementation that could be found on line\, nor there be any\nbenchmarks for these special tall and skinny LP s. We will describe\nsome variants and changes to the algorithm aiming f or practical\nperformancesto close this gap.\n\nWe also study a first orde r algorithm aimed for large scale LP\ns proposed by a group of researche rs from Google [2]\, [3] called\nPDLP. And compare it with Clarkson’s a lgorithm. DTSTAMP:20260804T183825Z END:VEVENT BEGIN:VEVENT UID:6a7231a18f404 DTSTART;TZID=America/Toronto:20260810T140000 SEQUENCE:0 TRANSP:TRANSPARENT DTEND;TZID=America/Toronto:20260810T150000 URL:https://uwaterloo.ca/combinatorics-and-optimization/events/masters-thes is-presentation-david-evangelista-backedge SUMMARY:Master's Thesis Presentation - David Evangelista - Backedge Graphs of\nTournaments: Algorithms and Complexity CLASS:PUBLIC DESCRIPTION:SPEAKER:\n David Evangelista\n\nSUPERVISOR(S):\n Joseph Cheriya n and Sophie Spirkl\n\nCOMMITTEE:\n Jane Gao\, Eric Blais\n\nLOCATION:\n M C 5417\n\nABSTRACT: \n\nA tournament $\\T=(V\,A)$ on $n$ vertices is an o rientation of the\ncomplete graph $K_n$. The backedge graph of $T$ with re spect to an\nordering of $V$ is the undirected graph on vertex set $V$ who se edge\nset corresponds to the arcs directed from a later vertex to an ea rlier\nvertex in the ordering. Backedge graphs provide concise\nrepresenta tions of the tournament. The algorithmic problem of\ndetermining whether a tournament admits a backedge graph in a given\nclass of undirected graphs varies in complexity\, and is often\nequivalent to computing parameters o f tournaments\, such as\ndegreewidth when the backedge graph has bounded maximum degree\n\\cite{Davot et al.\, 2023}. We extend the notion of degre ewidth by\nintroducing directional degreewidth\, which separately bounds t he\nleft-degrees and right-degrees of vertices in addition to bounding the \ntotal degrees. We obtain an algorithm for verifying bounds on the\ndirec tional degreewidth of the tournament\, whose runtime is polynomial\ntime w hen the total degree is unbounded\, or fixed-parameter tractable\ntime wit h respect to the total degree bound otherwise. We also provide\na polynomi al-time algorithm for computing a $P_3$-free backedge graph\nof a tourname nt\, if it exists. Together with existing results\, the\nlatter result set tles the complexity of determining whether a\ntournament admits an $H$-fre e backedge graph when $H$ is any graph on\nthree vertices. DTSTAMP:20260804T183825Z END:VEVENT BEGIN:VEVENT UID:6a7231a1907a6 DTSTART;TZID=America/Toronto:20260806T130000 SEQUENCE:0 TRANSP:TRANSPARENT DTEND;TZID=America/Toronto:20260806T160000 URL:https://uwaterloo.ca/combinatorics-and-optimization/events/phd-defense- leo-jung-preprocessing-hard-optimization SUMMARY:PhD Defense - Leo Jung - Preprocessing for Hard Optimization Proble ms\nAcross Structurally Diverse Models CLASS:PUBLIC DESCRIPTION:SPEAKER:\n\nLeo Jung\n\nLOCATION:\n MC 5029\n\nABSTRACT: \n\nD ifficulties in solving large-scale optimization problems often arise\nfrom structural pathologies such as ill-conditioning\, Hadamard\nill-posedness \, and degeneracy\, particularly due to the failure of\nconstraint qualifi cations. While standard algorithms often struggle to\naddress these issues \, preprocessing based on structural analysis\noffers an effective strateg y for overcoming such challenges. This\nthesis investigates several prepro cessing methods targeting various\nsources of these difficulties. \nIn Par t I\, we study a nonclassical\, average condition number of linear\nsystem s\, the $\\omega$-condition number. Our results demonstrate\nseveral advan tages of the $\\omega$-condition number over the classical\n$\\kappa$-cond ition number. First\, $\\omega$ provides a more accurate\nmeasure of the c onditioning of linear systems by more faithfully\ncapturing the effects of perturbations observed in practice. Second\,\n$\\omega$ exhibits superior numerical stability compared to $\\kappa$.\nThird\, when used in precondi tioner design\, $\\omega$ more effectively\npromotes eigenvalue clustering \, which is crucial for the efficiency of\niterative solvers. Finally\, th e analytical simplicity of $\\omega$\nenables the derivation of explicit o ptimality conditions\, allowing for\nclosed-form expressions of optimal pr econditioners under various\nframeworks\, including low rank updates of th e generalized Jacobian for\nsemismooth Newton methods and diagonal or bloc k-diagonal scaling. For\ndiagonal preconditioning\, we further include a c omparison between two\ndistinct notions of conditioning. \nIn Part II\, we first answer in the affirmative a long-standing open\nquestion of whether the smooth stress function admits local nonglobal\nminimizers. This quart ic nonconvex objective function arises in the\nexact recovery of a Euclide an distance matrix (EDM) of a given\nembedding dimension. By eliminating t he Hadamard ill-posedness caused\nby translation and rotation invariance\, we stabilize Newton's method\nand avoid singular Hessians. \\\\ \nWe then consider the single-element error correction problem as a case\nstudy. We first show that the standard nearest EDM formulation based\non minimizing the smooth stress function fails to recover the correct\nEDM in this sett ing. We then introduce divide-and-conquer strategies\nbased on facial redu ction. Our approach efficiently recovers the\ncorrect EDM with high accura cy\, and we further provide criteria\ncharacterizing the existence of mult iple solutions. \nIn Part III\, we relate FR to the analysis of the conver gence behaviour\nof a semismooth Newton method for projection onto a spect rahedron\,\ni.e.\, the intersection of a linear manifold and the semidefin ite cone.\nIn this process\, we derive an explicit formula for the project ion onto\na face of the semidefinite cone obtained via regularization and\ nanalyze pathologies that arise in the absence of strict feasibility.\nWe further show that ill-conditioning of the Jacobian near optimality\ncharac terizes the degeneracy of the projection point. \\\\ \nAs an application\, we consider a simplified Wasserstein barycenter\nproblem\, a well-known N P-hard problem. We compute the Wasserstein\nbarycenter by exploiting the s tructure of the linear constraints to\nobtain a facially reduced doubly no nnegative (DNN) relaxation. This\nreduction provides a natural splitting f or applying the symmetric\nalternating direction method of multipliers (sA DMM). The resulting\nalgorithm exploits structure in the subproblems to co mpute strong\nupper and lower bounds. In most of the instances\, we achiev e the small\ngap between these bounds\, which means that the original prob lem is\nsolved. DTSTAMP:20260804T183825Z END:VEVENT BEGIN:VEVENT UID:6a7231a1912e8 DTSTART;TZID=America/Toronto:20260805T140000 SEQUENCE:0 TRANSP:TRANSPARENT DTEND;TZID=America/Toronto:20260805T150000 URL:https://uwaterloo.ca/combinatorics-and-optimization/events/masters-thes is-presentation-martin-liu SUMMARY:Master's Thesis Presentation - Martin Liu CLASS:PUBLIC DESCRIPTION:SPEAKER:\n Martin Li\n\nSUPERVISOR(S):\n Vijay Bhattiprolu\n\nC OMITTEE:\n Jonathan Leake\, Levent Tuncel\n\nLOCATION:\n MC 6483\n\nABSTRA CT:\n\nThe $d$-dimensional Grothendieck constant is the smallest constant $K$\nsuch that \\begin{align*} \\sup\\left\\{\\sum_{i\,j=1}^n A_{ij}\\lang le\nu_i\,v_j\\rangle:u_i\,v_j\\in S^{d-1}\\right\\}\\le\nK\\cdot\\sup\\lef t\\{\\sum_{i\,j=1}^n\nA_{ij}x_iy_j:x_i\,y_j\\in\\{-1\,1\\}\\right\\} \\en d{align*}for any\n$n\\in\\mathbb{N}$ and any real $n\\times n$ matrix $A$. The inequality\nabove\, called the Grothendieck inequality\, has made a d eep impact in a\nvariety of areas such as functional analysis\, quantum in formation\ntheory\, and optimization. Determining the $d$-dimensional Grot hendieck\nconstant for any $d\\ge 3$ is a long-standing open problem.\n\nI n this paper\, we propose a worst operator in dimension 3\, whose\n$\\inft y\\to 1$ norm is conjectured to be $1/K_G(3)$. We study a related\nclass o f operators with nice geometric interpretations\, and we prove\nthe functi on $f:S^{d-1}\\to\\{-1\,1\\}$ corresponding to a hyperplane is\nuniquely o ptimal for this class\, with the isoperimetric inequality\nlying at the he art of our proof. DTSTAMP:20260804T183825Z END:VEVENT END:VCALENDAR