Three-steps iterative algorithms for mixed variational inequalities

Abstract

It is well known that the mixed variational inequalities are equivalent to the fixed point problems and the resolvent equations. Using this equivalence, we suggest and consider a new three-step iterative method for solving mixed variational inequalities. The new iterative method is obtained by using three-steps under suitable conditions. We prove that the new method is globally convergent. Our results can be viewed as significant extensions of the previously known results for mixed variational inequalities. Since mixed variational inequalities include variational inequalities as special cases, our method appears to be a new one for solving variational inequalities. Preliminary numerical experiments are included to illustrate the advantage and efficiency of the proposed method.