FULL LIPSCHITZIAN AND HOLDERIAN STABILITY IN OPTIMIZATION WITH APPLICATIONS TO MATHEMATICAL PROGRAMMING AND OPTIMAL CONTROL

被引：41

作者：

Mordukhovich, B. S. ^{[1
,2
]}

Nghia, T. T. A. ^{[3
]}

机构：

[1] Wayne State Univ, Dept Math, Detroit, MI 48202 USA

[2] King Fahd Univ Petr & Minerals, Dhahran 31261, Saudi Arabia

[3] Oakland Univ, Dept Math & Stat, Rochester, MI 48309 USA

来源：

SIAM JOURNAL ON OPTIMIZATION | 2014年 / 24卷 / 03期

基金：

美国国家科学基金会; 澳大利亚研究理事会;

关键词：

variational analysis and optimization; first-order and second-order generalized differentiation; Lipschitzian and Holderian stability; nonlinear programming; second-order growth and constraint qualifications; polyhedric constraints; optimal control; semilinear elliptic PDEs; PROX-REGULAR FUNCTIONS; TILT STABILITY; VARIATIONAL-INEQUALITIES; 2ND-ORDER ANALYSIS; SUBDIFFERENTIALS;

D O I：

10.1137/130906878

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The paper concerns a systematic study of full stability in general optimization models including its conventional Lipschitzian version as well as the new Holderian one. We derive various characterizations of both Lipschitzian and Holderian full stability in nonsmooth optimization, which are new in finite-dimensional and infinite-dimensional frameworks. The characterizations obtained are given in terms of second-order growth conditions and also via second-order generalized differential constructions of variational analysis. We develop effective applications of our general characterizations of full stability to conventional models of nonlinear programming, to optimization problems with polyhedric constraints in infinite dimensions, and to optimal control problems governed by semilinear elliptic PDEs.

引用

页码：1344 / 1381

页数：38

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