Set-Valued Resolvent Equations and Mixed Variational Inequalities

Variational-Like Inclusions and Resolvent Equations Involving Infinite Family of Set-Valued Mappings

Weighted Variational Inequalities with Set-valued Mappings

Because of their applications in economics, game theory, mathematical physics, operations research and other areas, many classes of vector variational inequalities were intensively studied. For existence of solutions, resolution methods or equivalence with equilibrium and optimization problems see, for example, [11], [14], [15], [19], [17] and the references therein. For the study of variationa...

A Descent Resolvent Method for Mixed Quasi Variational Inequalities

In this paper, we suggest and analyze a new iterative method for solving mixed quasi variational inequalities. The new iteration is obtained by searching the optimal step size along the integrated descent direction from two descent directions. Global convergence of the proposal method is proved under certain assumptions. Our results can be treated as refinement of previously known results. An e...

Forward-backward Resolvent Splitting Methods for General Mixed Variational Inequalities

We use the technique of updating the solution to suggest and analyze a class of new splitting methods for solving general mixed variational inequalities. It is shown that these modified methods converge for pseudomonotone operators, which is a weaker condition than monotonicity. Our methods differ from the known threestep forward-backward splitting of Glowinski, Le Tallec, and M. A. Noor for so...

Gap Functions and Global Error Bounds for Set-valued Mixed Variational Inequalities

In this paper, we introduce some gap functions for set-valued mixed variational inequalities under suitable conditions. We further use these gap functions to study global error bounds for the solutions of set-valued mixed variational inequalities in Hilbert spaces. The results presented in this paper generalize and improve some corresponding known results in literatures.