<?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%">Sihong Shao</style></author><author><style face="normal" font="default" size="100%">Dong Zhang</style></author><author><style face="normal" font="default" size="100%">Weixi Zhang</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">A simple iterative algorithm for maxcut</style></title><secondary-title><style face="normal" font="default" size="100%">Journal of Computational Mathematics</style></secondary-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://www.global-sci.org/intro/article_detail/jcm/23278.html</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">42</style></volume><pages><style face="normal" font="default" size="100%">1277-1304</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">We propose a simple iterative (SI) algorithm for the maxcut problem through fully using an equivalent continuous formulation. It does not need rounding at all and has advantages that all subproblems have explicit analytic solutions, the cut values are monotonically up- dated and the iteration points converge to a local optima in finite steps via an appropriate subgradient selection. Numerical experiments on G-set demonstrate the performance. In particular, the ratios between the best cut values achieved by SI and those by some ad- vanced combinatorial algorithms in [Ann. Oper. Res., 248 (2017), 365–403] are at least 0.986 and can be further improved to at least 0.997 by a preliminary attempt to break out of local optima.</style></abstract><issue><style face="normal" font="default" size="100%">5</style></issue></record></records></xml>