Metric Subregularity in Generalized Equations

被引：6

作者：

Marechal, Matthieu ^{[1
]}

机构：

[1] Univ Diego Portales, Fac Ingn & Ciencias, Inst Ciencias Basicas, Ejercito 441, Santiago, Chile

来源：

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS | 2018年 / 176卷 / 03期

关键词：

Metric subregularity; Nonsmooth analysis; Generalized equation; OPTIMALITY CONDITIONS; ERROR-BOUNDS; STABILITY;

D O I：

10.1007/s10957-018-1246-0

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：

In this article, we study the metric subregularity of generalized equations using a new tool of nonsmooth analysis. We obtain a sufficient condition for a generalized equation to be metrically subregular, which is not a necessary condition for metric regularity, using a subtle adjustment of the Mordukhovich coderivative. We apply these results to the study of the metric subregularity in a Cournot duopoly game.

引用

页码：541 / 558

页数：18

共 50 条

[1] Metric Subregularity in Generalized Equations
Matthieu Maréchal
Journal of Optimization Theory and Applications, 2018, 176 : 541 - 558
[2] Metric subregularity for proximal generalized equations in Hilbert spaces
Zheng, Xi Yin
Ng, Kung-Fu
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2012, 75 (03) : 1686 - 1699
[3] BCQ and Strong BCQ for Nonconvex Generalized Equations with Applications to Metric Subregularity
Huang, Liyun
He, Qinghai
Wei, Zhou
SET-VALUED AND VARIATIONAL ANALYSIS, 2014, 22 (04) : 747 - 762
[4] METRIC SUBREGULARITY AND CALMNESS FOR NONCONVEX GENERALIZED EQUATIONS IN BANACH SPACES
Zheng, Xi Yin
Ng, Kung Fu
SIAM JOURNAL ON OPTIMIZATION, 2010, 20 (05) : 2119 - 2136
[5] Metric Subregularity for Subsmooth Generalized Constraint Equations in Banach Spaces
He Qinghai
Yang Ji
Zhang Binbin
JOURNAL OF APPLIED MATHEMATICS, 2012,
[6] Error bounds and metric subregularity
Kruger, Alexander Y.
OPTIMIZATION, 2015, 64 (01) : 49 - 79
[7] Metric subregularity for composite-convex generalized equations in Banach spaces
Zheng, Xi Yin
Ouyang, Wei
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2011, 74 (10) : 3311 - 3323
[8] Metric subregularity and constraint qualifications for convex generalized equations in banach spaces
Zheng, Xi Yin
Ng, Kung Fu
SIAM JOURNAL ON OPTIMIZATION, 2007, 18 (02) : 437 - 460
[9] BCQ and Strong BCQ for Nonconvex Generalized Equations with Applications to Metric Subregularity
Liyun Huang
Qinghai He
Zhou Wei
Set-Valued and Variational Analysis, 2014, 22 : 747 - 762
[10] Directional Holder Metric Subregularity and Application to Tangent Cones
Huynh Van Ngai
Nguyen Huu Tron
Phan Nhat Tinh
JOURNAL OF CONVEX ANALYSIS, 2017, 24 (02) : 417 - 457

← 1 2 3 4 5 →