向量优化问题Benson真有效解最优性的二阶弱次微分刻画
Second-Order Weak Subdifferential Characterization of Optimality for Benson Properly Efficient Solutions in Vector Optimization Problems
DOI: 10.12677/pm.2026.162048, PDF,    科研立项经费支持
作者: 马 聪, 王其林*：重庆交通大学数学与统计学院，重庆；重庆交通大学复杂系统优化与智能控制重庆市高校重点实验室，重庆
关键词: 向量优化问题；Benson真有效解；最优性条件；二阶弱次微分；Vector Optimization Problems； Benson Properly Efficient Solutions； Optimality Conditions； Second-Order Weak Subdifferentials
摘要: 本文主要讨论向量优化问题Benson真有效解最优性条件。利用向量值映射的二阶弱次微分，在较弱的假设条件下，建立了向量优化问题Benson真有效解最优性必要条件和充分条件。同时，建立了复合优化问题最优解的2个充分条件。所获的主要结果改进并推广了文献中相应的结果。
Abstract: This paper mainly discusses the optimality conditions for Benson properly efficient solutions in vector optimization problems. Using the second-order weak subdifferential of vector-valued mappings, necessary and sufficient conditions for the optimality of Benson properly efficient solutions in vector optimization problems are established under weaker assumptions. Meanwhile, two sufficient conditions for the optimal solution of composite optimization problems are established. The main results obtained improve and generalize the corresponding results in the literature.
文章引用：马聪, 王其林. 向量优化问题Benson真有效解最优性的二阶弱次微分刻画[J]. 理论数学, 2026, 16(2): 194-199. https://doi.org/10.12677/pm.2026.162048

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