Unconstrained optimization reformulations of equilibrium problems
type: Item
instance of: scholarly article
title: Unconstrained optimization reformulations of equilibrium problems
zbMATH Open document ID: 1206.90185
publication date: 2009-11-11T00:00:00Z
review text: The goal of the paper is to extend the D-gap function corresponding to variational inequalities to a general equilibrium problem (EP, for short). First, the EP is reformulated as an unconstrained optimization problem by using the proposed gap function. Then the authors give conditions to guarantee that the stationary point of the unconstrained optimization problem is a solution of EP. Finally, they show that the unconstrained optimization problem has a bounded level set and provide global error bounds for EP. In the introduction examples of reformulations of EP as variational inequalities are given and it is presented a literature review on the popular approach to solving variational inequalities as equivalent minimization problems.
Mathematics Subject Classification ID: 90C30
Mathematics Subject Classification ID: 90C31
Mathematics Subject Classification ID: 90C33
Mathematics Subject Classification ID: 49J52
zbMATH DE Number: 5629505
zbMATH Keywords: equilibrium problems
zbMATH Keywords: D-gap function
zbMATH Keywords: error bound
zbMATH Keywords: unconstrained optimization
author: Liping Zhang
author: Jiye Han
reviewed by: Francisco Guerra Vazquez
MaRDI profile type: Publication
full work available at URL: s10114-008-7096-1
OpenAlex ID: W2405903239
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DOI: 10.1007/S10114-008-7096-1
published in: Acta Mathematica Sinica, English Series
description: scientific article; zbMATH DE number 5629505