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Abstract and Applied Analysis
Volume 2012, Article ID 792078, 16 pages
Research Article

Variant Gradient Projection Methods for the Minimization Problems

1Department of Mathematics, Tianjin Polytechnic University, Tianjin 300387, China
2Department of Information Management, Cheng Shiu University, Kaohsiung 833, Taiwan
3Center for General Education, Kaohsiung Medical University, Kaohsiung 807, Taiwan

Received 3 May 2012; Accepted 6 June 2012

Academic Editor: Jen-Chin Yao

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.


The gradient projection algorithm plays an important role in solving constrained convex minimization problems. In general, the gradient projection algorithm has only weak convergence in infinite-dimensional Hilbert spaces. Recently, H. K. Xu (2011) provided two modified gradient projection algorithms which have strong convergence. Motivated by Xu’s work, in the present paper, we suggest three more simpler variant gradient projection methods so that strong convergence is guaranteed.