Iterative methods for solving a class of monotone variational inequality problems with applications

Abstract

In this paper, we provide a more general regularization method for seeking a solution to a class of monotone variational inequalities in a real Hilbert space, where the regularizer is a hemicontinuous and strongly monotone operator. As a discretization of the regularization method, we propose an iterative method. We then prove that the proposed iterative method converges in norm to a solution of the class of monotone variational inequalities. We also apply our results to the constrained minimization problem and the minimum-norm fixed point problem for a generalized Lipschitz continuous and pseudocontractive mapping. The results presented in the paper improve and extend recent ones in the literature.