{"title":"Generalized Semi-infinite Polynomial Optimization and Semidefinite Programming Relaxations","authors":"Liguo Jiao, Jae Hyoung Lee, Tiến-Sơn Phạm","doi":"10.1007/s40306-024-00551-7","DOIUrl":null,"url":null,"abstract":"<div><p>This paper focuses on the study of a generalized semi-infinite programming, where the objective and the constraint functions are all real polynomials. We present a method for finding its global minimizers and global minimum using a hierarchy of semidefinite programming relaxations and prove the convergence result for the method. Numerical experiments are presented to show the efficiency of the proposed algorithm.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":"49 3","pages":"441 - 457"},"PeriodicalIF":0.3000,"publicationDate":"2024-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Mathematica Vietnamica","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1007/s40306-024-00551-7","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
This paper focuses on the study of a generalized semi-infinite programming, where the objective and the constraint functions are all real polynomials. We present a method for finding its global minimizers and global minimum using a hierarchy of semidefinite programming relaxations and prove the convergence result for the method. Numerical experiments are presented to show the efficiency of the proposed algorithm.
期刊介绍：
Acta Mathematica Vietnamica is a peer-reviewed mathematical journal. The journal publishes original papers of high quality in all branches of Mathematics with strong focus on Algebraic Geometry and Commutative Algebra, Algebraic Topology, Complex Analysis, Dynamical Systems, Optimization and Partial Differential Equations.
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