A new class of hybrid extragradient algorithms for solving quasi-equilibrium problems |
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Authors: | Jean Jacques Strodiot Thi Thu Van Nguyen Van Hien Nguyen |
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Institution: | 1. Institute for Computational Science and Technology, Ho Chi Minh City, Vietnam 2. Department of Mathematics, University of Namur, Namur, Belgium
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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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