A Predictor-Corrector Method for Solving Equilibrium Problems

Abstract

We suggest and analyze a predictor-corrector method for solving nonsmooth convex equilibrium problems based on the auxiliary problem principle. In the main algorithm each stage of computation requires two proximal steps. One step serves to predict the next point; the other helps to correct the new prediction. At the same time, we present convergence analysis under perfect foresight and imperfect one. In particular, we introduce a stopping criterion which gives rise to $\mathrm{\Delta }$-stationary points. Moreover, we apply this algorithm for solving the particular case: variational inequalities.