On Lipschitz-like continuity of a class of set-valued mappings

被引：8

作者：

Bednarczuk, E. M. ^{[1
,2
]}

Minchenko, L., I ^{[3
]}

Rutkowski, K. E. ^{[2
,4
]}

机构：

[1] Warsaw Univ Technol, Fac Math & Informat Sci, Warsaw, Poland

[2] Polish Acad Sci, Syst Res Inst, Warsaw, Poland

[3] Belarus State Univ Informat & Radioelect, Dept Informat, Minsk, BELARUS

[4] Cardinal Stefan Wyszynski Univ, Sch Exact Sci, Fac Math & Nat Sci, Warsaw, Poland

来源：

OPTIMIZATION | 2020年 / 69卷 / 12期

关键词：

Set-valued mappings; parametric optimization; relaxed constant rank constraint qualification; R-regularity; pseudo-Lipschitz continuity; Lipschitz-like continuity; Aubin property; STABILITY; SYSTEMS;

D O I：

10.1080/02331934.2019.1696339

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

We study set-valued mappings defined by solution sets of parametric systems of equalities and inequalities. We prove Lipschitz-like continuity of these mappings under relaxed constant rank constraint qualification.

引用

页码：2535 / 2549

页数：15

共 31 条

[1]

[Anonymous], 1984, MATH PROGRAMMING STU

[2]

[Anonymous], 1998, FUNDAMENTAL PRINCIPL

[3] LIPSCHITZ BEHAVIOR OF SOLUTIONS TO CONVEX MINIMIZATION PROBLEMS [J].

AUBIN, JP .

MATHEMATICS OF OPERATIONS RESEARCH, 1984, 9 (01) :87-111

[4] ON LIPSCHITZ-LIKE PROPERTY FOR POLYHEDRAL MOVING SETS [J].

Bednarczuk, E. ;

Rutkowski, K. .

SIAM JOURNAL ON OPTIMIZATION, 2019, 29 (04) :2504-2516

[5]

Bednarczuk EM, 2019, ARXIV190505581V2

[6]

BONNANS J. F., 2000, Perturbation Analysis of Optimization Problems

[7] STABILITY AND REGULAR POINTS OF INEQUALITY SYSTEMS [J].

BORWEIN, JM .

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 1986, 48 (01) :9-52

[8]

Clarke FH, 1983, OPTIMIZATION NONSMOO

[9]

DEMPE S., 2002, NONCON OPTIM ITS APP, V61

[10] Metric regularity and systems of generalized equations [J].

Dmitruk, Andrei V. ;

Kruger, Alexander Y. .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2008, 342 (02) :864-873

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