Predictor-Corrector Methods for General Regularized Nonconvex Variational Inequalities

This paper is devoted to the study of a new class of nonconvex variational inequalities, named general regularized nonconvex variational inequalities. By using the auxiliary principle technique, a new modified predictor-corrector iterative algorithm for solving general regularized nonconvex variational inequalities is suggested and analyzed. The convergence of the iterative algorithm is established under the partially relaxed monotonicity assumption. As a consequence, the algorithm and results presented in the paper overcome incorrect algorithms and results existing in the literature.