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

作者：Strodiot Jean Jacques^*; Thi Thu Van Nguyen; Van Hien Nguyen

来源：Journal of Global Optimization, 2013, 56(2): 373-397.

DOI：10.1007/s10898-011-9814-y

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

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.

• 出版日期2013-6