{"title":"Higher-order optimality conditions for nonregular multiobjective problem","authors":"A. S. Melo, L. B. Dos Santos, M. A. Rojas-Medar","doi":"10.1007/s10479-024-06198-9","DOIUrl":null,"url":null,"abstract":"<p>In this paper, we present necessary and sufficient optimality conditions for multiobjective problems with equality and inequality constraints defined in Banach spaces. We focus on the nonregular case when the linear independence qualification or Mangasarian-Fromovitz constraint qualification are not satisfied at the solution of the multiobjective problem. For this case, we present new generalized <i>p</i>-order necessary optimality conditions of Karush–Kuhn–Tucker type. The conditions subsume the classical conditions and give new and nontrivial conditions for the nonregular case. Our results were obtained from the theory of <i>p</i>-regularity, introduced by Brezhneva and Tret’yakov (SIAM J Control Optim 42:729-745, 2003). Some examples are presented to illustrate the results.</p>","PeriodicalId":8215,"journal":{"name":"Annals of Operations Research","volume":"119 1","pages":""},"PeriodicalIF":4.4000,"publicationDate":"2024-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annals of Operations Research","FirstCategoryId":"91","ListUrlMain":"https://doi.org/10.1007/s10479-024-06198-9","RegionNum":3,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"OPERATIONS RESEARCH & MANAGEMENT SCIENCE","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we present necessary and sufficient optimality conditions for multiobjective problems with equality and inequality constraints defined in Banach spaces. We focus on the nonregular case when the linear independence qualification or Mangasarian-Fromovitz constraint qualification are not satisfied at the solution of the multiobjective problem. For this case, we present new generalized p-order necessary optimality conditions of Karush–Kuhn–Tucker type. The conditions subsume the classical conditions and give new and nontrivial conditions for the nonregular case. Our results were obtained from the theory of p-regularity, introduced by Brezhneva and Tret’yakov (SIAM J Control Optim 42:729-745, 2003). Some examples are presented to illustrate the results.
期刊介绍：
The Annals of Operations Research publishes peer-reviewed original articles dealing with key aspects of operations research, including theory, practice, and computation. The journal publishes full-length research articles, short notes, expositions and surveys, reports on computational studies, and case studies that present new and innovative practical applications.
In addition to regular issues, the journal publishes periodic special volumes that focus on defined fields of operations research, ranging from the highly theoretical to the algorithmic and the applied. These volumes have one or more Guest Editors who are responsible for collecting the papers and overseeing the refereeing process.
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