Sufficient conditions for error bounds of difference functions and applications

被引：0
作者：
Nguyen Thi Van Hang
Jen-Chih Yao
机构：
[1] Vietnam Academy of Science and Technology,Institute of Mathematics
[2] China Medical University,Center for General Education
来源：
Journal of Global Optimization | 2016年 / 66卷
关键词：
d.c. inequalities system; Error bounds; Subdifferential; Exact penalty function; Lagrange multipliers; 49J52; 90C26; 90C46;
D O I：
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学科分类号：
摘要：
This paper establishes verifiable sufficient conditions for the existence of error bounds for the sub-level set of a difference function over an abstract constraint by applying a technique used by A. D. Ioffe. As a consequence, error bounds for constraint systems defined by d.c. inequalities and their applications in studying of exactness of the associated ℓ1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\ell _1$$\end{document} penalty function and existence of Lagrange multipliers as necessary optimality conditions are also investigated.
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页码：439 / 456
页数：17
相关论文
共 30 条
[1]  
Auslender AA(1988)Global regularity theorems Math. Oper. Res. 13 243-253
[2]  
Crouzeix J-P(1976)A new approach to Lagrange multipliers Math. Oper. Res. 1 165-174
[3]  
Clarke FH(1974)On the variational principle J. Math. Anal. Appl. 47 324-353
[4]  
Ekeland I(2015)On the problem of minimizing a difference of polyhedral convex functions under linear constraints J. Optim. Theory Appl. 49 263-265
[5]  
Hang NTV(1952)On approximate solutions of systems of linear inequalities J. Res. Nat. Bur. Standards Sect. B 251 61-69
[6]  
Yen ND(1979)Regular points of Lipschitz functions Trans. Am. Math. Soc. 17 245-250
[7]  
Hoffman AJ(1979)Necessary and sufficient conditions for a local minimum. 1: A reduction theorem and first order conditions SIAM J. Control Optim. 52 509-535
[8]  
Ioffe AD(2012)Exact penalty and error bounds in DC programming J. Glob. Optim. 30 408-425
[9]  
Ioffe AD(1992)On the linear convergence of descent methods for convex essentially smooth minimization SIAM J. Control Optim. 2 43-54
[10]  
Le Thi HA(1992)Error bound and convergence analysis of matrix splitting algorithms for the affine variational inequality problem SIAM J. Optim. 3 43-59
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