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