集值优化问题严格有效解的一、二阶最优性条件

First and Second Order Optimality Conditions for Strict Minimality in Set-valued Optimization

首先定义了集值优化问题的m阶局部严格有效解并在赋范空间中研究了解的一些性质.在一定条件下,利用Dini导算子和支撑函数确立了m≥1阶严格有效解存在的充分必要条件.

In this paper, the notion of local strict minimum of order rn （rn 〉1） for vector optimization problems is extended from single-valued maps to set-valued maps. Some properties and characterizations are then investigated in normed spaces. Furthermore, necessary and sufficient conditions for strict minimum of orders rn 〉1 are established by using Dini derivatives and support functions.