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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 313217, 11 pages
http://dx.doi.org/10.1155/2014/313217
Research Article

A Predictor-Corrector Method for Solving Equilibrium Problems

1School of Accounting, Zhejiang University of Finance and Economics, Hangzhou 310018, China
2Dalian University of Technology, Dalian 116024, China
3Dongbei University of Finance and Economics, Dalian 116025, China

Received 28 April 2014; Accepted 30 June 2014; Published 15 October 2014

Academic Editor: Adrian Petrusel

Copyright © 2014 Zong-Ke Bao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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 -stationary points. Moreover, we apply this algorithm for solving the particular case: variational inequalities.