<?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%">Ayache, Benhadid</style></author><author><style face="normal" font="default" size="100%">Khaled, Saoudi</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">A new parameterized logarithmic kernel function for linear optimization with a double barrier term yielding the best known iteration bound</style></title><secondary-title><style face="normal" font="default" size="100%">Communications in Mathematics</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://dml.cz/handle/10338.dmlcz/148259</style></url></web-urls></urls><publisher><style face="normal" font="default" size="100%">University of Ostrava</style></publisher><volume><style face="normal" font="default" size="100%">28</style></volume><pages><style face="normal" font="default" size="100%">27-41</style></pages><isbn><style face="normal" font="default" size="100%">1804-1388</style></isbn><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p style=&quot;text-align: justify;&quot;&gt;
	In this paper, we propose a large-update primal-dual interior point algorithm for linear optimization. The method is based on a new class of kernel functions which differs from the existing kernel functions in which it has a double barrier term. The investigation according to it yields the best known iteration bound O( √ n log(n) log( n ε )) for large-update algorithm with the special choice of its parameter m and thus improves the iteration bound obtained in Bai et al. [2] for large-update algorithm.
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