非凸集值优化问题弱Benson真有效解的高阶最优性条件

首先,给出了一些必要的基本概念和重要引理.其次,讨论了高阶广义切集的一些重要性质.最后,利用这些性质和Gerstewitz非凸分离泛函,在目标映射以及约束映射没有任何凸性假设的条件下,获得了带广义不等式约束的集值优化问题弱Benson真有效解的高阶必要和充分最优性条件.同时,给出例子说明了所获得的结果推广了文献中的相应...

Higher order optimality conditions for weakly Benson proper efficient solutions of nonconvex set-valued optimization problems

Firstly, some necessarily basic concepts and an important lemma were given. Secondly, some important properties of generalized higher-order tangent sets were discussed. Finally, by virtue of those properties and the Gerstewitz's nonconvex separation functional, necessary and sufficient optimality conditions were obtained for weakly Benson proper efficient solutions of set-valued optimization problems without any convexity assumption on objectiveand constraint mappings. Moreover, two examples were given to show that the result obtained is a generalization to the corresponding results in literatures.