Sufficient conditions for pseudo-Lipschitz property in convex semi-infinite vector optimization problems

被引：26
作者：
Chuong, Thai Doan [2 ]
Yao, Jen-Chih [1 ]
机构：
[1] Natl Sun Yat Sen Univ, Dept Appl Math, Kaohsiung 804, Taiwan
[2] Dong Thap Univ, Dept Math, Cao Lanh City, Dong Thap Prov, Vietnam
来源：
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2009年 / 71卷 / 12期
关键词：
Convex semi-infinite vector optimization; Efficient solution map; Pseudo-Lipschitz; Functional perturbations; Slater condition; METRIC REGULARITY; CONTINUITY; POSEDNESS; STABILITY;
D O I：
10.1016/j.na.2009.06.038
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper is devoted to the study of the pseudo-Lipschitz property of the efficient (Pareto) solution map for the perturbed convex semi-infinite vector optimization problem (CSVO). We establish sufficient conditions for the pseudo-Lipschitz property of the efficient solution map of (CSVO) under continuous perturbations of the right-hand side of the constraints and functional perturbations of the objective function. Examples are given to illustrate the obtained results. (C) 2009 Elsevier Ltd. All rights reserved.
引用
收藏
页码：6312 / 6322
页数：11
相关论文
共 25 条
[1]  
Aliprantis C.D., 2006, Infinite Dimensional Analysis
[2]  
BROSOWSKI B, 1984, SENSITIVITY STABILIT, P18
[3]   Metric regularity in convex semi-infinite optimization under canonical perturbations [J].
Canovas, M. J. ;
Klatte, D. ;
Lopez, M. A. ;
Parra, J. .
SIAM JOURNAL ON OPTIMIZATION, 2007, 18 (03) :717-732
[4]   Sufficient conditions for total ill-posedness in linear semi-infinite optimization [J].
Canovas, M. J. ;
Lopez, M. A. ;
Parra, J. ;
Toledo, F. J. .
EUROPEAN JOURNAL OF OPERATIONAL RESEARCH, 2007, 181 (03) :1126-1136
[5]   On the Lipschitz Modulus of the Argmin Mapping in Linear Semi-Infinite Optimization [J].
Canovas, M. J. ;
Gomez-Senent, F. J. ;
Parra, J. .
SET-VALUED ANALYSIS, 2008, 16 (5-6) :511-538
[6]   Lipschitz continuity of the optimal value via bounds on the optimal set in linear semi-infinite optimization [J].
Canovas, Maria J. ;
Lopez, Marco A. ;
Parra, Juan ;
Toledo, F. Javier .
MATHEMATICS OF OPERATIONS RESEARCH, 2006, 31 (03) :478-489
[7]   Metric regularity of semi-infinite constraint systems [J].
Cánovas, MJ ;
Dontchev, L ;
López, MA ;
Parra, J .
MATHEMATICAL PROGRAMMING, 2005, 104 (2-3) :329-346
[8]   Stability and well-posedness in linear semi-infinite programming [J].
Cánovas, MJ ;
López, MA ;
Parra, J ;
Todorov, MI .
SIAM JOURNAL ON OPTIMIZATION, 1999, 10 (01) :82-98
[9]   Stability of semi-infinite vector optimization problems under functional perturbations [J].
Chuong, T. D. ;
Huy, N. Q. ;
Yao, J. C. .
JOURNAL OF GLOBAL OPTIMIZATION, 2009, 45 (04) :583-595
[10]   Pseudo-Lipschitz property of linear semi-infinite vector optimization problems [J].
Chuong, T. D. ;
Huy, N. Q. ;
Yao, J. C. .
EUROPEAN JOURNAL OF OPERATIONAL RESEARCH, 2010, 200 (03) :639-644
123