A Third Order Dynamical System for Mixed Variational Inequalities

In this paper, we introduce and study a class of resolvent dynamical systems to investigate some inertial proximal methods for solving mixed variational inequalities. These proposed methods along with their discretizations and derived rates of convergences require only the monotonicity for mixed variational inequalities under some mild conditions. We establish the global asymptotically and exponentially stability of the solution of the resolvent dynamical system for monotone operators. Ideas and techniques of this paper may be extended for other classes of variational inequalities and equilibrium problems.