求解逆混合变分不等式问题的动力系统方法  

Dynamical System Approach for Solving Inverse Mixed Variational Inequality Problem

作　　者：罗馨缘 张欢 冯世强[1] LUO Xin-yuan;ZHANG Huan;FENG Shi-qiang(School of Mathematics and 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）》2024年第1期25-30,共6页Journal of China West Normal University(Natural Sciences)

基　　金：国家自然科学基金项目(11871059);大学生创新创业训练项目(cxcy2022022);大学生创新创业项目(xcy2023053)。

摘　　要：本文主要研究求解逆混合变分不等式问题的动力系统方法。首先,在强单调和Lipschitz连续性的假设下,通过借助广义f-投影算子的性质,得到逆混合变分不等式问题有唯一解的充分条件。进一步考虑一个动力系统方法来求解逆混合变分不等式问题,而且该动力系统具有唯一均衡点。最后,证明在强单调和Lipschitz连续性的条件下该动力系统的唯一均衡点是全局指数稳定的。This paper mainly focuses on the dynamical system approach for solving inverse mixed variational inequality problem.First,the sufficient conditions for the inverse mixed variational inequality problem to have a unique solution is obtained by means of the property of the generalized f-projection operators under the hypothesis of strong monotone and Lipschitz continuity.Furthermore,a dynamical system approach with a unique equilibrium point for solving inverse mixed variational inequality problem is considered.Finally,it is proved that the unique equilibrium point of the dynamical system is globally exponentially stable under the conditions of strong monotone and Lipschitz continuity.

关 键 词：逆混合变分不等式 广义f-投影算子 动力系统 均衡点 全局指数稳定 

分 类 号：O221[理学—运筹学与控制论]