解决二阶锥体互补问题的平滑惩罚法

IF 1.8 3区数学 Q1 Mathematics Journal of Global Optimization Pub Date : 2024-09-18 DOI:10.1007/s10898-024-01427-8

Chieu Thanh Nguyen, Jan Harold Alcantara, Zijun Hao, Jein-Shan Chen

{"title":"解决二阶锥体互补问题的平滑惩罚法","authors":"Chieu Thanh Nguyen, Jan Harold Alcantara, Zijun Hao, Jein-Shan Chen","doi":"10.1007/s10898-024-01427-8","DOIUrl":null,"url":null,"abstract":"<p>In this paper, we propose a smoothing penalty approach for solving the second-order cone complementarity problem (SOCCP). The SOCCP is approximated by a smooth nonlinear equation with penalization parameter. We show that any solution sequence of the approximating equations converges to the solution of the SOCCP under the assumption that the associated function of the SOCCP satisfies a uniform Cartesian-type property. We present a corresponding algorithm for solving the SOCCP based on this smoothing penalty approach, and we demonstrate the efficiency of our method for solving linear, nonlinear and tensor complementarity problems in the second-order cone setting.</p>","PeriodicalId":15961,"journal":{"name":"Journal of Global Optimization","volume":null,"pages":null},"PeriodicalIF":1.8000,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Smoothing penalty approach for solving second-order cone complementarity problems\",\"authors\":\"Chieu Thanh Nguyen, Jan Harold Alcantara, Zijun Hao, Jein-Shan Chen\",\"doi\":\"10.1007/s10898-024-01427-8\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>In this paper, we propose a smoothing penalty approach for solving the second-order cone complementarity problem (SOCCP). The SOCCP is approximated by a smooth nonlinear equation with penalization parameter. We show that any solution sequence of the approximating equations converges to the solution of the SOCCP under the assumption that the associated function of the SOCCP satisfies a uniform Cartesian-type property. We present a corresponding algorithm for solving the SOCCP based on this smoothing penalty approach, and we demonstrate the efficiency of our method for solving linear, nonlinear and tensor complementarity problems in the second-order cone setting.</p>\",\"PeriodicalId\":15961,\"journal\":{\"name\":\"Journal of Global Optimization\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.8000,\"publicationDate\":\"2024-09-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Global Optimization\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s10898-024-01427-8\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Global Optimization","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s10898-024-01427-8","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"Mathematics","Score":null,"Total":0}

引用次数: 0

摘要

本文提出了一种解决二阶锥体互补问题（SOCCP）的平滑惩罚方法。SOCCP 由一个带有惩罚参数的平滑非线性方程逼近。我们证明，在 SOCCP 的相关函数满足均匀笛卡尔类型属性的假设下，近似方程的任何解序列都会收敛到 SOCCP 的解。我们基于这种平滑惩罚方法提出了相应的 SOCCP 求解算法，并证明了我们的方法在二阶圆锥环境下求解线性、非线性和张量互补问题的效率。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

摘要图片

查看原文

微信好友朋友圈 QQ好友复制链接

本刊更多论文

Smoothing penalty approach for solving second-order cone complementarity problems

In this paper, we propose a smoothing penalty approach for solving the second-order cone complementarity problem (SOCCP). The SOCCP is approximated by a smooth nonlinear equation with penalization parameter. We show that any solution sequence of the approximating equations converges to the solution of the SOCCP under the assumption that the associated function of the SOCCP satisfies a uniform Cartesian-type property. We present a corresponding algorithm for solving the SOCCP based on this smoothing penalty approach, and we demonstrate the efficiency of our method for solving linear, nonlinear and tensor complementarity problems in the second-order cone setting.

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

Journal of Global Optimization 数学-应用数学

CiteScore

0.10

自引率

5.60%

发文量

137

审稿时长

6 months

期刊介绍： The Journal of Global Optimization publishes carefully refereed papers that encompass theoretical, computational, and applied aspects of global optimization. While the focus is on original research contributions dealing with the search for global optima of non-convex, multi-extremal problems, the journal’s scope covers optimization in the widest sense, including nonlinear, mixed integer, combinatorial, stochastic, robust, multi-objective optimization, computational geometry, and equilibrium problems. Relevant works on data-driven methods and optimization-based data mining are of special interest. In addition to papers covering theory and algorithms of global optimization, the journal publishes significant papers on numerical experiments, new testbeds, and applications in engineering, management, and the sciences. Applications of particular interest include healthcare, computational biochemistry, energy systems, telecommunications, and finance. Apart from full-length articles, the journal features short communications on both open and solved global optimization problems. It also offers reviews of relevant books and publishes special issues.