Abstract
AbstractWe study the extragradient method for solving quasi-equilibrium problems in Banach spaces, which generalizes the extragradient method for equilibrium problems and quasi-variational inequalities. We propose a regularization procedure which ensures strong convergence of the generated sequence to a solution of the quasi-equilibrium problem, under standard assumptions on the problem assuming neither any monotonicity assumption on the bifunction nor any weak continuity assumption of f in its arguments that in the many well-known methods have been used. Also, we give a necessary and sufficient condition for the solution set of the quasi-equilibrium problem to be nonempty and we show that, in this case, this iterative sequence converges strongly to a solution of the quasi-equilibrium problem. In other words, we prove strong convergence of the generated sequence to a solution of the quasi-equilibrium problem without assuming existence of a solution of the problem. Finally, we give an application of our main result to a generalized Nash equilibrium problem.
Publisher
Cambridge University Press (CUP)
Reference33 articles.
1. An existence result for quasi-equilibrium problems;Aussel;J. Convex Anal.,2017
2. Minimization of functions having Lipschitz continuous first partial derivatives
3. Application of Khobotov’s algorithm to variational inequalities and network equilibrium problems;Marcotte;INFOR Inf. Syst. Oper. Res.,1991
4. Extragradient algorithms extended to equilibrium problems¶
5. A remark on Ky Fan minimax principle;Brézis;Boll. Unione Mat. Ital.,1972
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