REGULARIZED GENERAL NONCONVEX MIXED EQUILIBRIUM PROBLEMS: PREDICTOR-CORRECTOR METHODS AND ALGORITHMS

In this paper, we consider a mixed equilibrium problem for non convex setting, called regularized general nonconvex mixed equilibrium problem. By using the auxiliary principle technique, we propose iterative algorithms and predictor-corrector methods for solving regularized general nonconvex mixed equilibrium problems. The convergence analysis of the proposed iterative algorithms requires either pseudomonotonicity or partially mixed relaxed and strong monotonicity property of the bifunction and the operator involved in regularized general nonconvex equilibrium problems. We have also investigated and pointed out that the results given in [M. A. Noor, K. I. Noor, E. Al-Said, Iterative methods for solving nonconvex equilibrium variational inequalities, Appl. Math. Inf. Sci. 6(2012) 65-69] are not valid. As a consequence of our main results, we provide the correct version of the results given in the above cited paper.