求解强伪单调拟均衡问题的动力系统方法  

Dynamic System Method for SolvingStrongly Pseudo-Monotone Quasi-Equilibrium Problems

作　　者：常浩 冯世强[1] 李军[1] CHANG Hao;FENG Shi-qiang;LI Jun(School of Mathematics&Information,China West Normal University,Nanchong Sichuan 637009,China)

机构地区：[1]西华师范大学数学与信息学院,四川南充637009

出　　处：《西华师范大学学报（自然科学版）》2022年第2期170-175,共6页Journal of China West Normal University(Natural Sciences)

基　　金：国家自然科学基金项目(11871059);西华师范大学校级创新训练项目(cxcy2021169)。

摘　　要：本文研究了强伪单调拟均衡问题。在Lipschitz连续性和强伪单调性的假设条件下,借助不动点理论,给出了拟均衡问题解存在唯一的充分条件。然后,考虑了一个动力系统方法来求解拟均衡问题,并说明了该动力系统具有唯一的均衡解。最后,证明了该均衡解在全局范围内是指数稳定的。该方法推广了均衡问题和拟变分不等式的动力系统方法。This paper talks about strongly pseudo-monotone quasi-equilibrium problems.Under the assumption of Lipschitz continuity and strong pseudo-monotonicity,sufficient conditions for the existence and uniqueness of solutions of quasi-equilibrium problems are obtained by means of fixed point theory.Then,a dynamical system method is considered to solve the quasi equilibrium problem,demonstrating the unique equilibrium solution of the dynamical system.Finally,it is proved that the equilibrium solution is globally exponentially stable.This method is an extension of the dynamic system method for equilibrium problems and quasi-variational inequalities.

关 键 词：均衡问题 拟均衡问题 强伪单调 动力系统 全局指数稳定 

分 类 号：O221[理学—运筹学与控制论]