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 [J].

HA, CW .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1979, 68 (01) :25-34

[12] Characterizing global optimality for DC optimization problems under convex inequality constraints [J].

Jeyakumar, V ;

Glover, BM .

JOURNAL OF GLOBAL OPTIMIZATION, 1996, 8 (02) :171-187

[13] Inequality systems and global optimization [J].

Jeyakumar, V ;

Rubinov, AM ;

Glover, BM ;

Ishizuka, Y .

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 [J].

Jeyakumar, V ;

Glover, BM .

MATHEMATICS OF OPERATIONS RESEARCH, 1995, 20 (04) :818-837

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

Jeyakumar, V .

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

[16] INEQUALITY SYSTEMS AND OPTIMIZATION [J].

JEYAKUMAR, V ;

GWINNER, 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 [J].

Wanka, G ;

Bot, RI .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2002, 275 (01) :354-368

[20]

Wanka G, 2002, OPERAT RES PROCEED, P255

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