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Journal of Global Optimization

, Volume 39, Issue 2, pp 247–260 | Cite as

An extension of gap functions for a system of vector equilibrium problems with applications to optimization problems

  • Jun Li
  • Nan-Jing Huang
Original Article

Abstract

In this paper, the notion of gap functions is extended from scalar case to vector one. Then, gap functions and generalized functions for several kinds of vector equilibrium problems are shown. As an application, the dual problem of a class of optimization problems with a system of vector equilibrium constraints (in short, OP) is established, the concavity of the dual function, the weak duality of (OP) and the saddle point sufficient condition are derived by using generalized gap functions.

Keywords

Vector equilibrium problem Optimization problem Generalized gap function The Lagrangian function Saddle point Weak duality 

2000 Mathematics Subject Classification

49J40 47J20 

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Copyright information

© Springer Science+Business Media, Inc. 2007

Authors and Affiliations

  1. 1.School of Mathematics and InformationChina West Normal UniversityNanchong, SichuanP.R. China
  2. 2.Department of MathematicsSichuan UniversityChengdu, SichuanP.R. China

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