On Quantitative Stability in Optimization and Optimal Control

被引：0
作者：
A. L. Dontchev
W. W. Hager
K. Malanowski
V. M. Veliov
机构：
[1] Mathematical Reviews,Department of Mathematics
[2] University of Florida,Systems Research Institute
[3] Polish Academy of Sciences,Institute of Mathematics and Informatics
[4] Bulgarian Acad. of Sc.,undefined
[5] Vienna University of Technology,undefined
来源：
Set-Valued Analysis | 2000年 / 8卷
关键词：
stability in optimization; generalized equations; Lipschitz continuity; mathematical programming; optimal control;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We study two continuity concepts for set-valued maps that play central roles in quantitative stability analysis of optimization problems: Aubin continuity and Lipschitzian localization. We show that various inverse function theorems involving these concepts can be deduced from a single general result on existence of solutions to an inclusion in metric spaces. As applications, we analyze the stability with respect to canonical perturbations of a mathematical program in a Hilbert space and an optimal control problem with inequality control constraints. For stationary points of these problems, Aubin continuity and Lipschitzian localization coincide; moreover, both properties are equivalent to surjectivity of the map of the gradients of the active constraints combined with a strong second-order sufficient optimality condition.
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页码：31 / 50
页数：19
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