A Second-Order Dynamical System for Solving Generalized Inverse Mixed Variational Inequality problems

Abstract: In this paper, we study a class of generalized inverse mixed variational inequality problems (GIMVIPs). We propose a novel projection-based second-order time-varying dynamical system for solving GIMVIPs. Under the assumptions that the underlying operators are strongly monotone and Lipschitz continuous, we establish the existence and uniqueness of solution trajectories and prove their global exponential convergence to the unique solution of the GIMVIP. Furthermore, a discrete-time realization of the continuous dynamical system is developed, resulting in an inertial projection algorithm. We show that the proposed algorithm achieves linear convergence under suitable choices of parameters. Finally, numerical experiments are presented to illustrate the effectiveness and convergence behavior of the proposed method in solving GIMVIPs.