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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 583710, 11 pages
http://dx.doi.org/10.1155/2013/583710
Research Article

A General Iterative Scheme Based on Regularization for Solving Equilibrium and Constrained Convex Minimization Problems

College of Science, Civil Aviation University of China, Tianjin 300300, China

Received 18 March 2013; Revised 25 May 2013; Accepted 28 June 2013

Academic Editor: Simeon Reich

Copyright © 2013 Ming Tian. 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

The present paper is divided into two parts. First, we introduce implicit and explicit iterative schemes based on the regularization for solving equilibrium and constrained convex minimization problems. We establish results on the strong convergence of the sequences generated by the proposed schemes to a common solution of minimization and equilibrium problem. Such a point is also a solution of a variational inequality. In the second part, as applications, we apply the algorithm to solve split feasibility problem and equilibrium problem.