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Journal of Function Spaces and Applications
Volume 2012, Article ID 678353, 26 pages
http://dx.doi.org/10.1155/2012/678353
Research Article

Hybrid Gradient-Projection Algorithm for Solving Constrained Convex Minimization Problems with Generalized Mixed Equilibrium Problems

1Department of Mathematics, Scientific Computing Key Laboratory of Shanghai Universities, Shanghai Normal University, Shanghai 200234, China
2Center for General Education, Kaohsiung Medical University, Kaohsiung 80708, Taiwan

Received 16 July 2012; Accepted 8 September 2012

Academic Editor: Hong-Kun Xu

Copyright © 2012 Lu-Chuan Ceng and Ching-Feng Wen. 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

It is well known that the gradient-projection algorithm (GPA) for solving constrained convex minimization problems has been proven to have only weak convergence unless the underlying Hilbert space is finite dimensional. In this paper, we introduce a new hybrid gradient-projection algorithm for solving constrained convex minimization problems with generalized mixed equilibrium problems in a real Hilbert space. It is proven that three sequences generated by this algorithm converge strongly to the unique solution of some variational inequality, which is also a common element of the set of solutions of a constrained convex minimization problem, the set of solutions of a generalized mixed equilibrium problem, and the set of fixed points of a strict pseudocontraction in a real Hilbert space.