Set-valued mixed quasi-variational inequalities and implicit resolvent equations

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...

An Iterative Method for Generalized Set-Valued Nonlinear Mixed Quasi-Variational Inequalities

This paper presents an iterative method for solving the generalized nonlinear set-valued mixed quasi-variational inequality, a problem class that was introduced by Huang, Bai, and Kang, [Comp. Math. Appl., 40, 2000]. The method incorporates step size controls that enable application to problems where certain set-valued mappings do not always map to nonempty closed bounded sets.

New Approximate Schemes for Generalized General Set-valued Mixed Quasi Variational Inequalities

In this paper, we suggest and consider a class of new three-step approximation schemes for generalized general set-valued mixed quasi variational inequalities. We also consider and analyze a new class of extragradienttype methods for solving generalized set-valued variational inequalities. The proposed methods include several new and known methods as special cases. Our results present a signifi...

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...