{"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}
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Abstract
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.
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