二元全局优化的更紧低估器

IF 0.9 Q2 MATHEMATICS

Afrika Matematika Pub Date : 2025-01-13 DOI:10.1007/s13370-024-01235-z

Mohand Ouanes

{"title":"二元全局优化的更紧低估器","authors":"Mohand Ouanes","doi":"10.1007/s13370-024-01235-z","DOIUrl":null,"url":null,"abstract":"<div><p>We propose in this paper a tighter underestimator for <span>\\(C^{2}\\)</span>-nonconvex bivariate functions. We show that it is tighter than the classical <span>\\(\\alpha -\\)</span>BB underestimator. A branch and bound algorithm with this tighter underestimator is developed to solve bivariate global optimzation problems. The triangulation is used as an exhaustive subdivision, and a convex/concave test is added to accelerate the convergence of our branch and bound algorithm.</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":"36 1","pages":""},"PeriodicalIF":0.9000,"publicationDate":"2025-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Tighter underestimator for bivariate global optimization\",\"authors\":\"Mohand Ouanes\",\"doi\":\"10.1007/s13370-024-01235-z\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We propose in this paper a tighter underestimator for <span>\\\\(C^{2}\\\\)</span>-nonconvex bivariate functions. We show that it is tighter than the classical <span>\\\\(\\\\alpha -\\\\)</span>BB underestimator. A branch and bound algorithm with this tighter underestimator is developed to solve bivariate global optimzation problems. The triangulation is used as an exhaustive subdivision, and a convex/concave test is added to accelerate the convergence of our branch and bound algorithm.</p></div>\",\"PeriodicalId\":46107,\"journal\":{\"name\":\"Afrika Matematika\",\"volume\":\"36 1\",\"pages\":\"\"},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2025-01-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Afrika Matematika\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s13370-024-01235-z\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Afrika Matematika","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1007/s13370-024-01235-z","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

本文提出了\(C^{2}\) -非凸二元函数的一个更严格的低估量。我们证明它比经典的\(\alpha -\) BB低估器更紧。针对二元全局优化问题，提出了一种具有这种严格低估量的分支定界算法。将三角剖分作为穷举细分，并加入凸/凹检验，加快了分支定界算法的收敛速度。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Tighter underestimator for bivariate global optimization

We propose in this paper a tighter underestimator for \(C^{2}\)-nonconvex bivariate functions. We show that it is tighter than the classical \(\alpha -\)BB underestimator. A branch and bound algorithm with this tighter underestimator is developed to solve bivariate global optimzation problems. The triangulation is used as an exhaustive subdivision, and a convex/concave test is added to accelerate the convergence of our branch and bound 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

Afrika Matematika MATHEMATICS-

CiteScore

2.00

自引率

9.10%

发文量