Resolvent dynamical systems and mixed variational inequalities

Abstract

In this paper, we use the dynamical systems technique to suggest and investigate some inertial proximal methods for solving mixed variational inequalities and related optimization problems. It is proved that the convergence analysis of the proposed methods requires only the monotonicity. Some special cases are also considered. Our method of proof is very simple as compared with other techniques. Ideas and techniques of this paper may be extended for other classes of variational inequalities and equilibrium problems.

Absolute Value Variational Inequalities and Dynamical Systems

“…Hence the equilibrium problems in different branches of pure and applied sciences which are studied in the framework of variational inequalities, can now be considered in the more general framework of projected dynamical systems. Projected dynamical systems are effective in the development of many efficient numerical techniques for approximating the solutions of variational inequalities and related nonlinear problems, see [3,6,10,11]. The global asymptotic stability of the projected dynamical systems has also been studied by Noor [33] and Xia and Wang [46].…”