集值映射的Epi-导数及其应用(英文)

On an Epiderivative of Set-Valued Maps and Its Application

在本文里,集值映射的Epi-导数被引入,它可以认作是实值Lipschitz函数的ClaLrke-广义方向导数的推广,同时它的一些性质也被研究.进一步地,利用这个Epi-导数集值映射的次微分被定义并研究它的性质.作为其应用,我们给出了集值优化问题的一些(必要或充分)最优性条件.

An epiderivative for a set-valued map is introduced in this paper that can be regarded as an extension to Clarke generalized directional derivative for a real-valued Lipschitz function and its properties are discussed. Furthermore, the subdifferential of a general set-valued map is defined in terms of this epiderivative. As an application, some (necessary and/or sufficient) optimality conditions of set-valued optimization problems are presented based on obtained results.