参数非光滑优化的微分稳定性

本文研究了含有向量参数的非光滑优化问题的极值函数或叫做边缘函数的连续性及某种意义下的微分性质。给出了目标函数及不等式约束为李普希兹函数,等式约束为连续可微函数,并且带有闭凸约束集C的非凸非光滑问题的最优值函数的几种方向导数的界,把[4],[1]中关于一个参数的单边扰动推广到向量参数的扰动,亦可认为是把[2]由光滑函数类推广到李普希兹函数类。

Differential Stability for Parametric Nonsmooth Optimization

This paper studies the continuous and differential properties of marginal functions or extremal value functions of nonsmooth optimization problems with vecter parameter . It gives the bounds of some directional derivatives of marginal functions for nonsmooth and nonconvex problems in which the target function and inequality constraints are Lipschitz and equality constraints are smooth. It is an extension of [ 1 ], and [ 4 ] from one-side perturbation to vecter parametric perturbation . It also considers an extension of [1] from smooth functions to nonsmooth functions.