In this paper, we study the convergence of a proximal point method for solving quasi-equilibrium problems (QEP) in Hilbert spaces. We extent the method proposed by Moudafi [Proximal point algorithm extended to equilibrium problems. J Nat Geom. 1999;15(1-2):91–100] and Iusem and Sosa [Iterative algorithms for equilibrium problems. Optimization. 2003;52(3):301–316] to the more general context of quasi-equilibrium problems. In our method a quasi-equilibrium problem is solved by computing a solution of an equilibrium problem at each iteration. We obtain weak convergence of the sequence to a solution of the QEP under some mild assumptions. Some encouraging numerical experiments are presented to show the performance of the method.

在本文中，我们研究了求解希尔伯特空间中准平衡问题（QEP）的近点法的收敛性。我们扩展了 Moudafi [Proximal point algorithm 扩展到平衡问题的方法。国家地理杂志。1999;15(1-2):91–100] 和 Iusem 和 Sosa [平衡问题的迭代算法。优化。2003;52(3):301–316] 到准平衡问题的更一般背景。在我们的方法中，通过在每次迭代中计算平衡问题的解来解决准平衡问题。在一些温和的假设下，我们获得了序列对 QEP 解的弱收敛。提出了一些令人鼓舞的数值实验来展示该方法的性能。