Abstract
In this paper, we suggest and analyze a new three-step iterative method for solving mixed variational inequalities. The new iterate is obtained by using a descent direction. We prove that the new method is globally convergent under suitable mild conditions. 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.