Stability of set-valued mappings in infinite dimensions: Point criteria and applications

被引：52
作者：
Mordukhovich, BS
Shao, YH
机构：
[1] Department of Mathematics, Wayne State University, Detroit
来源：
SIAM JOURNAL ON CONTROL AND OPTIMIZATION | 1997年 / 35卷 / 01期
关键词：
infinite-dimensional systems; stability; metric regularity; optimization; nonsmooth analysis; set-valued solution maps; generalized differentiation; sensitivity;
D O I：
10.1137/S0363012994278171
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
This paper dears with effective characterizations of stability and regularity properties of set-valued mappings in infinite dimensions, which are of great importance for applications to many aspects in optimization and control. The main purpose is to obtain verifiable necessary and sufficient conditions for these properties that are expressed in terms of constructive generalized differential structures at reference points and are convenient for applications. Based on advanced techniques in nonsmooth analysis, new dual criteria are proven in this direction under minimal assumptions. Applications of such point conditions are given to sensitivity analysis for parametric constraint and variational systems which describe sets of feasible and optimal solutions to various optimization and related problems.
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页码：285 / 314
页数：30
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