A New System of Multivalued Mixed Variational Inequality Problem

Xi Li,Xue-Song Li

doi:10.1155/2014/982606

Abstract

We consider a new system of multivalued mixed variational inequality problem, which includes some known systems of variational inequalities as special cases. Under suitable conditions, the existence of solutions for the system of multivalued mixed variational inequality problem and the convergence of iterative sequences generated by the generalizedf-projection algorithm are proved. A perturbational algorithm for solving a special case of multivalued mixed variational inequality problem is formally constructed. The results concerned with the existence of solutions and the convergence of iterative sequences generated by the perturbational algorithm are also given. Some known results are improved and generalized.

Highlights

Variational inequalities are known to be very useful tool to formulate and investigate various network equilibrium problems arising in economic, management, and engineering
Let H be a real Hilbert space with scalar product and norm denoted by ⟨⋅, ⋅⟩ and ‖ ⋅ ‖, respectively
The property of generalized f-projection operator plays an important role in solving the system of multivalued mixed variational inequality problem

Summary

A New System of Multivalued Mixed Variational Inequality Problem

We consider a new system of multivalued mixed variational inequality problem, which includes some known systems of variational inequalities as special cases. The existence of solutions for the system of multivalued mixed variational inequality problem and the convergence of iterative sequences generated by the generalized f-projection algorithm are proved. A perturbational algorithm for solving a special case of multivalued mixed variational inequality problem is formally constructed. The results concerned with the existence of solutions and the convergence of iterative sequences generated by the perturbational algorithm are given. Some known results are improved and generalized

Introduction

Preliminaries

The Multivalued Mixed Variational Inequality System

Existence and Convergence Theorems