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

Jean Strodiot (), Thi Nguyen () and Nguyen Van ()

Journal of Global Optimization, 2013, vol. 56, issue 2, 373-397

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. Copyright Springer Science+Business Media, LLC. 2013

Keywords: Quasi-equilibrium problems; Quasi-variational inequalities; Hybrid extragradient methods; Generalized Nash equilibrium problems; 49J40; 65K10; 91A12 (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (9)

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DOI: 10.1007/s10898-011-9814-y

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