A new iterative method for variational inequalities
The paper presents a new iterative method for variational inequalities. The solution of the elliptic variational inequality (by the projection technique) is equivalent to a fixed point problem. This alternative formulation has played a fundamental and significant part in developing several numerical methods for solving variational inequalities and related optimization problems. Since the convergence of these methods requires that the operator is both strongly monotone and Lipschitz continuous and as it is very difficult to evaluate the projection of the operator, the authors had to develop other techniques including the technique of updating of solution. Main results: A new iterative method is obtained by using three steps under suitable conditions. It is shown that the convergence of the proposed method requires only pseudomonotonicity. The new method is globally convergent. Finally an example is presented to illustrate the efficiency and advantage of the proposed new iterative method.
strongly monotone and Lipschitz continuous operator
scientific article; zbMATH DE number 5115437