A new class of hybrid extragradient algorithms for solving quasi-equilibrium problems

Research output: Contribution to journalArticle

Abstract

Generalized Nash equilibrium problems are important examples of quasi-equilibrium problems. The aim of this paper is to study a general class of algorithms for solving such problems. The method is a hybrid extragradient method whose second step consists in finding a descent direction for the distance function to the solution set. This is done thanks to a linesearch. Two descent directions are studied and for each one several steplengths are proposed to obtain the next iterate. A general convergence theorem applicable to each algorithm of the class is presented. It is obtained under weak assumptions: the pseudomonotonicity of the equilibrium function and the continuity of the multivalued mapping defining the constraint set of the quasi-equilibrium problem. Finally some preliminary numerical results are displayed to show the behavior of each algorithm of the class on generalized Nash equilibrium problems.

Original languageEnglish
Pages (from-to)373-397
Number of pages25
JournalJournal of Global Optimization
Volume56
Issue number2
DOIs
Publication statusPublished - 1 Jun 2013

Fingerprint

Quasiequilibrium Problems
Equilibrium Problem
Descent
Nash Equilibrium
Pseudomonotonicity
Extragradient Method
Multivalued Mapping
Line Search
Distance Function
Hybrid Method
Solution Set
Iterate
Convergence Theorem
Numerical Results
Class
Equilibrium problem
Quasi-equilibrium
Hybrid algorithm
Nash equilibrium

Keywords

  • Generalized Nash equilibrium problems
  • Hybrid extragradient methods
  • Quasi-equilibrium problems
  • Quasi-variational inequalities

Cite this

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abstract = "Generalized Nash equilibrium problems are important examples of quasi-equilibrium problems. The aim of this paper is to study a general class of algorithms for solving such problems. The method is a hybrid extragradient method whose second step consists in finding a descent direction for the distance function to the solution set. This is done thanks to a linesearch. Two descent directions are studied and for each one several steplengths are proposed to obtain the next iterate. A general convergence theorem applicable to each algorithm of the class is presented. It is obtained under weak assumptions: the pseudomonotonicity of the equilibrium function and the continuity of the multivalued mapping defining the constraint set of the quasi-equilibrium problem. Finally some preliminary numerical results are displayed to show the behavior of each algorithm of the class on generalized Nash equilibrium problems.",
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A new class of hybrid extragradient algorithms for solving quasi-equilibrium problems. / Strodiot, Jean-Jacques; Nguyen, Thi Thu Van; Nguyen, Van Hien.

In: Journal of Global Optimization, Vol. 56, No. 2, 01.06.2013, p. 373-397.

Research output: Contribution to journalArticle

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