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Pure Mathematics 2026
向量优化问题Benson真有效解最优性的二阶弱次微分刻画
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Abstract:
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。
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.
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