{"title":"具有可能空解集的多目标最优控制问题中的微分稳定性","authors":"N. T. Toan, L. Q. Thuy","doi":"10.1007/s40306-023-00522-4","DOIUrl":null,"url":null,"abstract":"<div><p>This paper studies the first-order behavior of the weak optimal value mapping in a parametric multi-objective discrete optimal control problem under linear state equations, where the solution set may be empty. By establishing an abstract result on the <span>\\(\\varepsilon \\)</span>-weak subdifferential of the weak optimal value mapping in a parametric multi-objective mathematical programming problem with an inclusion constraint, we derive a formula for computing the <span>\\(\\varepsilon \\)</span>-weak subdifferential of the weak optimal value mapping in a parametric multi-objective discrete optimal control problem. The obtained results are proved directly without using scalarization techniques.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":null,"pages":null},"PeriodicalIF":0.3000,"publicationDate":"2024-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Differential Stability in a Multi-Objective Optimal Control Problems with a Possibly Empty Solution Set\",\"authors\":\"N. T. Toan, L. Q. Thuy\",\"doi\":\"10.1007/s40306-023-00522-4\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>This paper studies the first-order behavior of the weak optimal value mapping in a parametric multi-objective discrete optimal control problem under linear state equations, where the solution set may be empty. By establishing an abstract result on the <span>\\\\(\\\\varepsilon \\\\)</span>-weak subdifferential of the weak optimal value mapping in a parametric multi-objective mathematical programming problem with an inclusion constraint, we derive a formula for computing the <span>\\\\(\\\\varepsilon \\\\)</span>-weak subdifferential of the weak optimal value mapping in a parametric multi-objective discrete optimal control problem. The obtained results are proved directly without using scalarization techniques.</p></div>\",\"PeriodicalId\":45527,\"journal\":{\"name\":\"Acta Mathematica Vietnamica\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.3000,\"publicationDate\":\"2024-01-03\",\"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/s40306-023-00522-4\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Mathematica Vietnamica","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1007/s40306-023-00522-4","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
Differential Stability in a Multi-Objective Optimal Control Problems with a Possibly Empty Solution Set
This paper studies the first-order behavior of the weak optimal value mapping in a parametric multi-objective discrete optimal control problem under linear state equations, where the solution set may be empty. By establishing an abstract result on the \(\varepsilon \)-weak subdifferential of the weak optimal value mapping in a parametric multi-objective mathematical programming problem with an inclusion constraint, we derive a formula for computing the \(\varepsilon \)-weak subdifferential of the weak optimal value mapping in a parametric multi-objective discrete optimal control problem. The obtained results are proved directly without using scalarization techniques.
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.