可导集值向量优化的最优性条件(英文)

Optimality Conditions of Vector Optimization Involving Derivable Set-valued Maps

本文研究了集值优化问题的最优性条件.引入了集值映射Clark切导数的概念,利用Clark切导数,给出了集值优化弱有效解的一个最优性必要条件.建立了集值映射伪凸和拟凸的概念,并获得了弱有效解的两个最优性充分条件.

The aim of this paper is to develop the optimality conditions of set-valued optimization. We introduce Clark＇s tangent derivative of the set-valued map. Then we develop a necessary optimality condition of set-valued optimization based on Clark＇s tangent derivative of set- valued map. We establish the concepts of pseudoconvex and qusiconvex of the set-valued map, and then investigate two sufficient optimality conditions for the weak efficient solution.