The Gap Functions and Error Bounds of Solutions of a Class of Set-valued Mixed Variational Inequality and Related Algorithms

Abstract

In this paper, we extend a class of generalizedized mixed variational inequality problem, and we study the gap functions, error bounds of solutions and related algorithms of a class of set-valued mixed variational inequalities. In order to solve these problems, we establish the corresponding generalized resolvent equations and prove the equivalence between these problems. Finally, we give three iterative algorithms and analyze the convergence of algorithms.