求解逆变分不等式的二阶动力系统方法  

Second-order Dynamical System Methodfor Solving Inverse Variational Inequalities

作　　者：郭洋俊骁 李军[1,2] GUO Yang-jun-xiao;LI Jun(School of Mathematics&Information,China West Normal University,Nanchong Sichuan 637009,China;Key Laboratory of Optimization Theory and Applications at China West Normal University of Sichuan Province,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 [2]西华师范大学最优化理论与应用四川省高校重点实验室,四川南充637009

出　　处：《西华师范大学学报（自然科学版）》2024年第4期375-380,共6页Journal of China West Normal University(Natural Sciences)

基　　金：国家自然科学基金项目(11871059)。

摘　　要：在强单调和Lipschitz连续性的条件下,在Euclidean空间中提出了一种新的求解逆变分不等式的二阶动力系统方法。首先,给出了逆变分不等式解的存在性和唯一性。进一步地,改进了Vuong等构建的二阶动力系统,并以此来求解逆变分不等式,而且在Lipschitz连续性的条件下,该动力系统具有唯一强全局解。最后,利用在强单调和Lipschitz连续性的假设下逆变分不等式唯一解的误差界,来证明此条件下该动力系统的唯一强全局解是指数收敛的。In this paper,a new second-order dynamical system method for solving inverse variational inequalities is proposed in Euclidean space under the conditions of strong monotonicity and Lipschitz continuity.Firstly,the existence and uniqueness of solutions to inverse variational inequalities is given.Then,a second-order dynamical system method based on Vuong et al.is improved to solve inverse variational inequalities.Furthermore,the dynamical system has a unique strong global solution under the condition of Lipschitz continuity.Finally,the error bound of the unique solution to inverse variational inequalities is employed to prove that the unique strong global solution of the dynamical system is exponentially convergent under the assumption of strong monotonicity and Lipschitz continuity.

关 键 词：强单调 LIPSCHITZ连续性 逆变分不等式 二阶动力系统 强全局解 指数收敛 

分 类 号：O221[理学—运筹学与控制论]