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Abstract and Applied Analysis
Volume 2014, Article ID 264965, 19 pages
Research Article

Steepest-Descent Approach to Triple Hierarchical Constrained Optimization Problems

1Department of Mathematics, Shanghai Normal University, and Scientific Computing Key Laboratory of Shanghai Universities, Shanghai 200234, China
2Department of Information Management, Yuan Ze University, Chung-Li 32003, Taiwan
3Department of Information Management, and Innovation Center for Big Data and Digital Convergence, Yuan Ze University, Chung-Li 32003, Taiwan
4Center for Fundamental Science, Kaohsiung Medical University, Kaohsiung 807, Taiwan

Received 4 May 2014; Accepted 31 July 2014; Published 31 August 2014

Academic Editor: Jong Kyu Kim

Copyright © 2014 Lu-Chuan Ceng 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.


We introduce and analyze a hybrid steepest-descent algorithm by combining Korpelevich’s extragradient method, the steepest-descent method, and the averaged mapping approach to the gradient-projection algorithm. It is proven that under appropriate assumptions, the proposed algorithm converges strongly to the unique solution of a triple hierarchical constrained optimization problem (THCOP) over the common fixed point set of finitely many nonexpansive mappings, with constraints of finitely many generalized mixed equilibrium problems (GMEPs), finitely many variational inclusions, and a convex minimization problem (CMP) in a real Hilbert space.