<?xml version="1.0" encoding="UTF-8"?><xml><records><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></records></xml>