集值优化问题Benson真有效解的高阶Fritz John型最优性条件

摘要

This paper deals with higher-order Fritz John type optimality conditions for Benson proper efficient solutions of set-valued optimization problems. By virtue of the higher-order tangent sets introduced by Aubin and Frankowska and the separation theorem of convex sets, we obtained higher-order Fritz John type necessary and suffi-cient optimality conditions for Benson proper efficient solutions of set-valued optimization problems with generalized inequality constraints under the assumption of cone-convexlike maps.%本文讨论的是集值优化问题Benson真有效解的高阶Fritz John型最优性条件,利用Aubin和Fraukowska引入的高阶切集和凸集分离定理,在锥-似凸映射的假设条件下,获得了带广义不等式约束的集值优化问题Benson真有效解的高阶Fritz John型必要和充分性条件.