Metric subregularity for proximal generalized equations in Hilbert spaces

被引：18

作者：

Zheng, Xi Yin ^{[1
]}

Ng, Kung-Fu ^{[2
,3
]}

机构：

[1] Yunnan Univ, Dept Math, Kunming 650091, Peoples R China

[2] Chinese Univ Hong Kong, Dept Math, Shatin, Hong Kong, Peoples R China

[3] Chinese Univ Hong Kong, IMS, Shatin, Hong Kong, Peoples R China

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2012年 / 75卷 / 03期

关键词：

Metric subregularity; Prox-regularity; Coderivative; Normal cone; GLOBAL ERROR-BOUNDS; REGULAR FUNCTIONS; SUBSMOOTH SETS; CALMNESS; MULTIFUNCTIONS;

D O I：

10.1016/j.na.2011.07.004

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we introduce and consider the concept of the prox-regularity of a multifunction. We mainly study the metric subregularity of a generalized equation defined by a proximal closed multifunction between two Hilbert spaces. Using proximal analysis techniques, we provide sufficient and/or necessary conditions for such a generalized equation to have the metric subregularity in Hilbert spaces. We also establish the results of Robinson-Ursescu theorem type for prox-regular multifunctions. (C) 2011 Elsevier Ltd. All rights reserved.

引用

页码：1686 / 1699

页数：14

共 42 条

[21] REGULAR POINTS OF LIPSCHITZ FUNCTIONS [J].

IOFFE, AD .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1979, 251 (JUL) :61-69

[22] On metric and calmness qualification conditions in subdifferential calculus [J].

Ioffe, Alexander D. ;

Outrata, Jiri V. .

SET-VALUED ANALYSIS, 2008, 16 (2-3) :199-227

[23] VERIFIABLE CONDITIONS FOR OPENNESS AND REGULARITY OF MULTIVALUED MAPPINGS IN BANACH-SPACES [J].

JOURANI, A ;

THIBAULT, L .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1995, 347 (04) :1255-1268

[24]

LEWIS A, 1997, GEN CONVEXITY GEN MO, P75

[25] Global error bounds for convex multifunctions and applications [J].

Li, W ;

Singer, I .

MATHEMATICS OF OPERATIONS RESEARCH, 1998, 23 (02) :443-462

[26] COMPLETE CHARACTERIZATION OF OPENNESS, METRIC REGULARITY, AND LIPSCHITZIAN PROPERTIES OF MULTIFUNCTIONS [J].

MORDUKHOVICH, B .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1993, 340 (01) :1-35

[27]

Mordukhovich B. S., 2006, Grundlehren der mathematischen Wissenschaften, V330

[28]

Ng K.F., 1973, MATH P CAMB, V74, P61

[29] Error bounds for lower semicontinuous functions in normed spaces [J].

Ng, KF ;

Zheng, XY .

SIAM JOURNAL ON OPTIMIZATION, 2001, 12 (01) :1-17

[30] Local differentiability of distance functions [J].

Poliquin, RA ;

Rockafellar, RT ;

Thibault, L .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2000, 352 (11) :5231-5249

← 1 2 3 4 5 →