Farkas-type results with conjugate functions

被引：35

作者：

Bot, RI ^{[1
]}

Wanka, G ^{[1
]}

机构：

[1] Tech Univ Chemnitz, Fac Math, D-09107 Chemnitz, Germany

来源：

SIAM JOURNAL ON OPTIMIZATION | 2005年 / 15卷 / 02期

关键词：

Farkas-type results; conjugate duality; finitely and infinitely many convex constraints;

D O I：

10.1137/030602332

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We present some new Farkas-type results for inequality systems involving a finite as well as an infinite number of convex constraints. For this, we use two kinds of conjugate dual problems, namely an extended Fenchel-type dual problem and the recently introduced Fenchel Lagrange dual problem. For the latter, which is a "combination" of the classical Fenchel and Lagrange duals, the strong duality is established.

引用

页码：540 / 554

页数：15

共 22 条

[11] SYSTEMS OF CONVEX INEQUALITIES
HA, CW
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1979, 68 (01) : 25 - 34
[12] Characterizing global optimality for DC optimization problems under convex inequality constraints
Jeyakumar, V
Glover, BM
[J]. JOURNAL OF GLOBAL OPTIMIZATION, 1996, 8 (02) : 171 - 187
[13] Inequality systems and global optimization
Jeyakumar, V
Rubinov, AM
Glover, BM
Ishizuka, Y
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1996, 202 (03) : 900 - 919
[14] Nonlinear extensions of Farkas' lemma with applications to global optimization and least squares
Jeyakumar, V
Glover, BM
[J]. MATHEMATICS OF OPERATIONS RESEARCH, 1995, 20 (04) : 818 - 837
[15] Characterizing set containments involving infinite convex constraints and reverse-convex constraints
Jeyakumar, V
[J]. SIAM JOURNAL ON OPTIMIZATION, 2003, 13 (04) : 947 - 959
[16] INEQUALITY SYSTEMS AND OPTIMIZATION
JEYAKUMAR, V
GWINNER, J
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1991, 159 (01) : 51 - 71
[17] Rockafellar, 2015, CONVEX ANAL
[18] RUBINOV AM, 1995, J CONVEX ANAL, V2, P309
[19] Multiobjective duality for convex ratios
Wanka, G
Bot, RI
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2002, 275 (01) : 354 - 368
[20] Wanka G, 2002, OPERAT RES PROCEED, P255

← 1 2 3 →