A new iterative method for variational inequalities

摘要

It is well known that the variational inequalities are equivalent to the fixed point problems. Using this equivalence, we suggest and consider a new three-step iterative method for solving 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 variational inequalities. Preliminary numerical experiments are included to illustrate the advantage and efficiency of the proposed method.