Necessary and sufficient constraint qualifications for solvability of systems of infinite convex inequalities

被引：51

作者：

Goberna, M. A. ^{[2
]}

Jeyakumar, V. ^{[1
]}

Lopez, M. A. ^{[2
]}

机构：

[1] Univ New S Wales, Dept Appl Math, Sydney, NSW 2052, Australia

[2] Univ Alicante, Dept Stat & Operat Res, Alicante, Spain

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2008年 / 68卷 / 05期

基金：

澳大利亚研究理事会;

关键词：

D O I：

10.1016/j.na.2006.12.014

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we present constraint qualifications which completely characterize the Farkas-Minkowski and the locally Farkas-Minkowski convex (possibly infinite) inequality systems posed in topological vector spaces. The number of constraints and the dimension of the linear space are arbitrary (possibly infinite). The constraint qualifications considered in this paper are expressed in terms of the solvability of certain parametric convex (linear) systems and the uniform strong duality or the uniform min-max duality relative to the Lagrange (Haar) dual problems of suitable convex (linear) parametric optimization problems. (c) 2007 Elsevier Ltd. All rights reserved.

引用

页码：1184 / 1194

页数：11

共 13 条

[1] An alternative formulation for a new closed cone constraint qualification [J].

Bot, RI ;

Wanka, G .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2006, 64 (06) :1367-1381

[2]

Burachik RS, 2005, J CONVEX ANAL, V12, P279

[3] A new geometric condition for Fenchel's duality in infinite dimensional spaces [J].

Burachik, RS ;

Jeyakumar, V .

MATHEMATICAL PROGRAMMING, 2005, 104 (2-3) :229-233

[4]

Dinh N, 2006, J CONVEX ANAL, V13, P113

[5]

DINH N, IN PRESS ESAIM CONTR

[6]

GOBERNA MA, 1998, LINEAR SEMI INFINITE

[7] UNIFORM DUALITY IN SEMI-INFINITE CONVEX-OPTIMIZATION [J].

JEROSLOW, RG .

MATHEMATICAL PROGRAMMING, 1983, 27 (02) :144-154

[8] The strong conical hull intersection property for convex programming [J].

Jeyakumar, V .

MATHEMATICAL PROGRAMMING, 2006, 106 (01) :81-92

[9] Characterizing set containments involving infinite convex constraints and reverse-convex constraints [J].

Jeyakumar, V .

SIAM JOURNAL ON OPTIMIZATION, 2003, 13 (04) :947-959

[10]

JEYAKUMAT V, 2004, AMR048 U N S WAL

← 1 2 →