{"title":"Strict Efficiency in Vector Optimization Via a Directional Curvature Functional","authors":"José Cerda-Hernández, Alberto Ramos","doi":"10.1007/s00245-025-10220-2","DOIUrl":null,"url":null,"abstract":"<div><p>We derive new necessary and sufficient conditions for strict efficiency in vector optimization problems for non-smooth mappings. Unlike other approaches, our conditions are described in terms of a suitable directional curvature functional that allows us to derive no-gap second-order optimality conditions in an abstract setting. Our approach allows us to apply our results even when classical assumptions such as the second-order regularity conditions to the feasible set fail, extending the applicability of our approach. As applications to mathematical programming, we provide new primal and dual Karush-Kuhn-Tucker (KKT) second-order necessary and sufficient conditions. We provide some examples to illustrate our findings.</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"91 1","pages":""},"PeriodicalIF":1.6000,"publicationDate":"2025-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Mathematics and Optimization","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s00245-025-10220-2","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
We derive new necessary and sufficient conditions for strict efficiency in vector optimization problems for non-smooth mappings. Unlike other approaches, our conditions are described in terms of a suitable directional curvature functional that allows us to derive no-gap second-order optimality conditions in an abstract setting. Our approach allows us to apply our results even when classical assumptions such as the second-order regularity conditions to the feasible set fail, extending the applicability of our approach. As applications to mathematical programming, we provide new primal and dual Karush-Kuhn-Tucker (KKT) second-order necessary and sufficient conditions. We provide some examples to illustrate our findings.
期刊介绍：
The Applied Mathematics and Optimization Journal covers a broad range of mathematical methods in particular those that bridge with optimization and have some connection with applications. Core topics include calculus of variations, partial differential equations, stochastic control, optimization of deterministic or stochastic systems in discrete or continuous time, homogenization, control theory, mean field games, dynamic games and optimal transport. Algorithmic, data analytic, machine learning and numerical methods which support the modeling and analysis of optimization problems are encouraged. Of great interest are papers which show some novel idea in either the theory or model which include some connection with potential applications in science and engineering.
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