P*(κ)-水平线性互补问题的高效多参数核函数大和小更新方法

Mousaab Bouafia, Adnan Yassine
{"title":"P*(κ)-水平线性互补问题的高效多参数核函数大和小更新方法","authors":"Mousaab Bouafia, Adnan Yassine","doi":"10.1051/ro/2023094","DOIUrl":null,"url":null,"abstract":"In this paper, we propose the first efficient multi parametric kernel function with logarithmic barrier term. A class of polynomial interior-point algorithms for P*(κ)-horizontal linear complementarity problem based on this kernel function, with parameters pi > 0 for all i ∈ 1, 2, , m, are presented. Then by using some simple analysis tools, we present a primal-dual interior point method (IPM) for P*(κ)-horizontal linear complementarity problems based on this kernel function. At the same time, we derive the complexity bounds small and large-update methods, respectively. In particular, if we take many different values of the parameters, we obtain the best known iteration bounds for the algorithms with large- and small-update methods are derived, namely, O((1 + 2κ)√n(log n)log n/ϵ) and O((1 + 2κ)√n log n/ϵ) respectively. We illustrate the performance of the proposed kernel function by some numerical results that are derived by applying our algorithm.","PeriodicalId":20872,"journal":{"name":"RAIRO Oper. Res.","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"An efficient multi parametric kernel function for large and small-update methods interior point algorithm for P*(κ)-horizontal linear complementarity problem\",\"authors\":\"Mousaab Bouafia, Adnan Yassine\",\"doi\":\"10.1051/ro/2023094\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we propose the first efficient multi parametric kernel function with logarithmic barrier term. A class of polynomial interior-point algorithms for P*(κ)-horizontal linear complementarity problem based on this kernel function, with parameters pi > 0 for all i ∈ 1, 2, , m, are presented. Then by using some simple analysis tools, we present a primal-dual interior point method (IPM) for P*(κ)-horizontal linear complementarity problems based on this kernel function. At the same time, we derive the complexity bounds small and large-update methods, respectively. In particular, if we take many different values of the parameters, we obtain the best known iteration bounds for the algorithms with large- and small-update methods are derived, namely, O((1 + 2κ)√n(log n)log n/ϵ) and O((1 + 2κ)√n log n/ϵ) respectively. We illustrate the performance of the proposed kernel function by some numerical results that are derived by applying our algorithm.\",\"PeriodicalId\":20872,\"journal\":{\"name\":\"RAIRO Oper. Res.\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-05-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"RAIRO Oper. Res.\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1051/ro/2023094\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"RAIRO Oper. Res.","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1051/ro/2023094","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0

摘要

本文提出了第一个具有对数屏障项的高效多参数核函数。基于该核函数,对所有i∈1,2,,m,给出了一类参数pi > 0的P*(κ)-水平线性互补问题的多项式内点算法。然后利用一些简单的分析工具,给出了基于该核函数的P*(κ)-水平线性互补问题的原始-对偶内点法。同时,分别推导了小更新方法和大更新方法的复杂度界限。特别是,如果我们取许多不同的参数值,我们得到了大更新方法和小更新方法的最知名迭代界,即O((1 + 2κ)√n(log n)log n/ λ)和O((1 + 2κ)√n log n/ λ)。我们通过应用我们的算法得到的一些数值结果来说明所提出的核函数的性能。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
An efficient multi parametric kernel function for large and small-update methods interior point algorithm for P*(κ)-horizontal linear complementarity problem
In this paper, we propose the first efficient multi parametric kernel function with logarithmic barrier term. A class of polynomial interior-point algorithms for P*(κ)-horizontal linear complementarity problem based on this kernel function, with parameters pi > 0 for all i ∈ 1, 2, , m, are presented. Then by using some simple analysis tools, we present a primal-dual interior point method (IPM) for P*(κ)-horizontal linear complementarity problems based on this kernel function. At the same time, we derive the complexity bounds small and large-update methods, respectively. In particular, if we take many different values of the parameters, we obtain the best known iteration bounds for the algorithms with large- and small-update methods are derived, namely, O((1 + 2κ)√n(log n)log n/ϵ) and O((1 + 2κ)√n log n/ϵ) respectively. We illustrate the performance of the proposed kernel function by some numerical results that are derived by applying our algorithm.
求助全文
通过发布文献求助,成功后即可免费获取论文全文。 去求助
来源期刊
自引率
0.00%
发文量
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信