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Abstract and Applied Analysis
Volume 2012, Article ID 310801, 17 pages
http://dx.doi.org/10.1155/2012/310801
Research Article

Algorithmic Approach to a Minimization Problem

1Department of Mathematics, Tianjin Polytechnic University, Tianjin 300387, China
2Department of Mathematics and RINS, Gyeongsang National University, Jinju 660-701, Republic of Korea
3Department of Information Management, Cheng Shiu University, Kaohsiung 833, Taiwan

Received 27 April 2012; Accepted 7 May 2012

Academic Editor: Rudong Chen

Copyright © 2012 Yonghong Yao 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 first construct an implicit algorithm for solving the minimization problem , where is the intersection set of the solution set of some equilibrium problem, the fixed points set of a nonexpansive mapping, and the solution set of some variational inequality. Further, we suggest an explicit algorithm by discretizing this implicit algorithm. We prove that the proposed implicit and explicit algorithms converge strongly to a solution of the above minimization problem.