A dual view of equilibrium problems

被引：38

作者：

Bigi, Giancarlo ^{[1
]}

Castellani, Marco ^{[2
]}

Kassay, Gabor ^{[3
]}

机构：

[1] Univ Pisa, Dipartimento Informat, I-56127 Pisa, Italy

[2] Univ Laquila, Dipartimento Sistemi & Ist Econ, I-67040 Laquila, Italy

[3] Univ Babes Bolyai, Fac Matemat Informat, RO-400084 Cluj Napoca, Romania

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2008年 / 342卷 / 01期

关键词：

equilibrium problem; Lagrangian function; dual equilibrium problem; Fenchel duality;

D O I：

10.1016/j.jmaa.2007.11.034

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The aim of this paper is to introduce and study a dual problem associated to a generalized equilibrium problem (GEP). We show that the solutions of (GEP) and its dual are strictly related to the saddle points of an associated Lagrangian function, and, under some suitable conditions, to the solutions of a family of parametric optimization problems and their dual problems. Our results allow us to show that well-known concepts and results from duality theory of some important particular cases of (GEP) like variational inequalities and optimization problems can be recovered. (C) 2007 Elsevier Inc. All rights reserved.

引用

页码：17 / 26

页数：10

共 16 条

[1] Coercivity conditions for equilibrium problems [J].

Bianchi, M ;

Pini, R .

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2005, 124 (01) :79-92

[2] Existence of equilibria via Ekeland's principle [J].

Bianchi, M ;

Kassay, G ;

Pini, R .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2005, 305 (02) :502-512

[3] A note on equilibrium problems with properly quasimonotone bifunctions [J].

Bianchi, M ;

Pini, R .

JOURNAL OF GLOBAL OPTIMIZATION, 2001, 20 (01) :67-76

[4] Generalized monotone bifunctions and equilibrium problems [J].

Bianchi, M ;

Schaible, S .

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 1996, 90 (01) :31-43

[5]

Blum E., 1993, MATH STUDENT, V63, P1

[6]

Giannessi F., 1998, NEW TRENDS MATH PROG

[7]

Hiriart-Urruty J. B., 1996, CONVEX ANAL MINIMIZA, V305

[8] New existence results for equilibrium problems [J].

Iusem, AN ;

Sosa, W .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2003, 52 (02) :621-635

[9] Factorization of Minty and Stampacchia variational inequality systems [J].

Kassay, G ;

Kolumbán, J ;

Páles, Z .

EUROPEAN JOURNAL OF OPERATIONAL RESEARCH, 2002, 143 (02) :377-389

[10]

Kassay G., 2000, EQUILIBRIUM PROBLEM

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