On error bounds for systems

被引：0
作者：
Liu, C. G. [1 ]
Ng, K. F. [2 ]
机构：
[1] Jinan Univ, Dept Math, Guangzhou 510632, Guangdong, Peoples R China
[2] Chinese Univ Hong Kong, Inst Math Sci, Dept Math, Shatin, Hong Kong, Peoples R China
来源：
TOP | 2015年 / 23卷 / 02期
基金：
中国国家自然科学基金;
关键词：
Error bound; Strongly positive matrix; Upper Dini-directional derivative; Descent/directional descent condition; LOWER SEMICONTINUOUS FUNCTIONS; SUFFICIENT CONDITIONS;
D O I：
10.1007/s11750-014-0353-9
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 paper we discuss some conditions ensuring the error bound property for a family of functions. By virtual of matrix theory on strongly positive matrices we provide some descent/directional descent conditions ensuring the existence of error bounds for systems of functions. These conditions relax the descent requirement for functions and provide useful methods for establishing error bounds.
引用
收藏
页码：552 / 566
页数：15
相关论文
共 28 条
[1]  
[Anonymous], GEN CONVEXITY
[2]   On the sensitivity analysis of Hoffman constants for systems of linear inequalities [J].
Azé, D ;
Corvellec, JN .
SIAM JOURNAL ON OPTIMIZATION, 2002, 12 (04) :913-927
[3]  
Aze D., 2003, ESAIM P, V13, P1, DOI DOI 10.1051/proc:2003004
[4]   Sufficient conditions for error bounds and applications [J].
Bosch, P ;
Jourani, A ;
Henrion, R .
APPLIED MATHEMATICS AND OPTIMIZATION, 2004, 50 (02) :161-181
[5]   Error bound results for convex inequality systems via conjugate duality [J].
Bot, Radu Ioan ;
Csetnek, Ernoe Robert .
TOP, 2012, 20 (02) :296-309
[6]   Nonlinear error bounds for lower semicontinuous functions on metric spaces [J].
Corvellec, Jean-Noel ;
Motreanu, Viorica V. .
MATHEMATICAL PROGRAMMING, 2008, 114 (02) :291-319
[7]   ON APPROXIMATE SOLUTIONS OF SYSTEMS OF LINEAR INEQUALITIES [J].
HOFFMAN, AJ .
JOURNAL OF RESEARCH OF THE NATIONAL BUREAU OF STANDARDS, 1952, 49 (04) :263-265
[8]   On first- and second-order conditions for error bounds [J].
Huang, LR ;
Ng, KF .
SIAM JOURNAL ON OPTIMIZATION, 2004, 14 (04) :1057-1073
[9]   Error bounds in metric spaces and application to the perturbation stability of metric regularity [J].
Huynh Van Ngai ;
Thera, Michel .
SIAM JOURNAL ON OPTIMIZATION, 2008, 19 (01) :1-20
[10]   Global error bounds for piecewise convex polynomials [J].
Li, Guoyin .
MATHEMATICAL PROGRAMMING, 2013, 137 (1-2) :37-64
123