无约束向量集值优化中的二次最优性条件

Second-order Optimality Conditions in Vector Set-velued Optimization without Constrains

考虑集值向量优化中的二次最优性条件.引进了新的集值映射的二次切上导数概念,并利用这个概念给出了在无约束条件下弱有效点对,Henig有效点对,整体有效点对,f-有效点对的充分和必要条件,以及Benson有效点必要条件.

In this paper, we consider second - order optimality conditions in vector set - valued optimization, we present new second- order epiderivatives for set - valued maps. By these concepts, we give a necessary and sufficient condition for a weakly efficient solution, a Henig efficient solution, a global efficient solution, an f- efficient solution, respectively, to a vector set- valued optimizaition problem without constraints, and a necessary