集值优化问题的高阶最优性条件
Higher-Order Optimality Conditions for Set-Valued Optimization Problems
DOI: 10.12677/pm.2025.1512295, PDF,    科研立项经费支持
作者: 朱俊哲：重庆交通大学数学与统计学院，重庆；薛小维*：重庆文理学院数学与人工智能学院，重庆
关键词: 广义高阶弱切上图导数；最优性条件；向量优化；集优化；Higher-Order Generalized Tangent Epiderivative； Optimality Condition； Vector Optimization； Set Optimization
摘要: 本文利用由高阶切集所构建的高阶导数，建立了向量优化准则下集值优化问题弱极小元的最优性充分条件和必要条件，在上集合少序关系下分别介绍了集值优化问题在集优化准则下弱极大元和严格弱极大元的一些性质，并得到了严格弱极大元的最优性充分条件和必要条件。
Abstract: This article establishes the sufficient and necessary optimality conditions for weakly minimal elements of set-valued optimization problems under the vector optimization criterion, using the higher-order derivatives constructed by higher-order tangent sets. Under the upper set less order relation, it introduces some properties of weakly maximal elements and strictly weakly maximal solutions of set-valued optimization problems under the set optimization criterion respectively, and obtains the sufficient and necessary optimality conditions for strictly weakly maximal elements.
文章引用：朱俊哲, 薛小维. 集值优化问题的高阶最优性条件[J]. 理论数学, 2025, 15(12): 69-76. https://doi.org/10.12677/pm.2025.1512295

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