{"title":"Higher-Order Efficiency Conditions for Vector Nonsmooth Optimization Problems Using the Higher-Order Gâteaux Derivatives","authors":"Tran Van Su, Dinh Dieu Hang","doi":"10.1007/s41980-024-00904-w","DOIUrl":null,"url":null,"abstract":"<p>In this article, we investigate the higher-order nonsmooth optimality conditions for vector optimization problems with inequality, equality and set constraints in terms of the higher-order Gâteaux derivatives. First, we propose various higher-order Mangasarian–Fromovitz nonsmooth constraint qualifications for such problems. Second, we formulate higher-order KKT-type necessary optimality conditions for the local weak efficient solutions of the nonsmooth vector equilibrium problem with constraints (CVEP) and its special cases. An application of the result to the resources assignment problem with set, inequality, equality constraints is derived. Under some suitable assumptions involving a set constraint, the higher-order nonsmooth necessary optimality conditions become the higher-order sufficient optimality conditions via the higher-order directional/Gâteaux derivatives.</p>","PeriodicalId":9395,"journal":{"name":"Bulletin of The Iranian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2024-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Bulletin of The Iranian Mathematical Society","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s41980-024-00904-w","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
In this article, we investigate the higher-order nonsmooth optimality conditions for vector optimization problems with inequality, equality and set constraints in terms of the higher-order Gâteaux derivatives. First, we propose various higher-order Mangasarian–Fromovitz nonsmooth constraint qualifications for such problems. Second, we formulate higher-order KKT-type necessary optimality conditions for the local weak efficient solutions of the nonsmooth vector equilibrium problem with constraints (CVEP) and its special cases. An application of the result to the resources assignment problem with set, inequality, equality constraints is derived. Under some suitable assumptions involving a set constraint, the higher-order nonsmooth necessary optimality conditions become the higher-order sufficient optimality conditions via the higher-order directional/Gâteaux derivatives.
期刊介绍：
The Bulletin of the Iranian Mathematical Society (BIMS) publishes original research papers as well as survey articles on a variety of hot topics from distinguished mathematicians. Research papers presented comprise of innovative contributions while expository survey articles feature important results that appeal to a broad audience. Articles are expected to address active research topics and are required to cite existing (including recent) relevant literature appropriately. Papers are critically reviewed on the basis of quality in its exposition, brevity, potential applications, motivation, value and originality of the results. The BIMS takes a high standard policy against any type plagiarism. The editorial board is devoted to solicit expert referees for a fast and unbiased review process.
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