{"title":"Scalar representations and Hausdorff continuity of solution mappings to parametric set optimization problems via set less order relations","authors":"Lam Quoc Anh , Pham Thanh Duoc , Ha Manh Linh","doi":"10.1016/j.orl.2024.107071","DOIUrl":null,"url":null,"abstract":"<div><p>This paper aims to formulate scalar representations and stability conditions for parametric set<span> optimization problems involving set less order relations. We first introduce new nonlinear scalarization functions for sets and discuss their properties, and then they are utilized to establish scalar representations for solutions to such problems. Finally, we study sufficient conditions for the Hausdorff continuity of approximate solution mappings to the reference problems.</span></p></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2024-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Operations Research Letters","FirstCategoryId":"91","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0167637724000075","RegionNum":4,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"OPERATIONS RESEARCH & MANAGEMENT SCIENCE","Score":null,"Total":0}
引用次数: 0
Abstract
This paper aims to formulate scalar representations and stability conditions for parametric set optimization problems involving set less order relations. We first introduce new nonlinear scalarization functions for sets and discuss their properties, and then they are utilized to establish scalar representations for solutions to such problems. Finally, we study sufficient conditions for the Hausdorff continuity of approximate solution mappings to the reference problems.
期刊介绍：
Operations Research Letters is committed to the rapid review and fast publication of short articles on all aspects of operations research and analytics. Apart from a limitation to eight journal pages, quality, originality, relevance and clarity are the only criteria for selecting the papers to be published. ORL covers the broad field of optimization, stochastic models and game theory. Specific areas of interest include networks, routing, location, queueing, scheduling, inventory, reliability, and financial engineering. We wish to explore interfaces with other fields such as life sciences and health care, artificial intelligence and machine learning, energy distribution, and computational social sciences and humanities. Our traditional strength is in methodology, including theory, modelling, algorithms and computational studies. We also welcome novel applications and concise literature reviews.
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