Proximal-Resolvent Methods for Mixed Variational Inequalities

Abstract

It is well-known that the mixed variational inequalities are equivalent to the fixed point problem. We use this alternative equivalent formulation to suggest and analyze some new proximal resolvent methods for solving mixed variational inequalities. We also study the convergence of these new methods under some mild conditions. These new iterative methods include the projection, extragradient and proximal methods as special cases. Results obtained in this paper represent a refinement and improvement of the previously known results.