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2011, 1(3): 341-359. doi: 10.3934/naco.2011.1.341

## Extragradient-projection method for solving constrained convex minimization problems

 1 Department of Mathematics, Shanghai Normal University, Scientific Computing Key Laboratory of Shanghai Universities, Shanghai 200234, China 2 Department of Mathematics, Aligarh Muslim University, Aligarh 202 002, India 3 Kaohsiung Medical University, Kaohsiung Medical University, Kaohsiung 80708, Taiwan

Received  April 2011 Revised  June 2011 Published  September 2011

In this paper, we introduce an iterative process for finding a common element of the set of fixed points of a nonexpansive mapping and the set of solutions of a constrained convex minimization problem for a Fr\'{e}chet differentiable function. The iterative process is based on the so-called extragradient-projection method. We derive several weak convergence results for two sequences generated by the proposed iterative process. On the other hand, by applying the viscosity approximation method and the additional projection method (namely, the CQ method) to the extragradient-projection method, respectively, we also provide two modifications of the extragradient-projection method to obtain two strong convergence theorems. The results of this paper represent the supplement, improvement, extension and development of some known results given in the literature.
Citation: Luchuan Ceng, Qamrul Hasan Ansari, Jen-Chih Yao. Extragradient-projection method for solving constrained convex minimization problems. Numerical Algebra, Control & Optimization, 2011, 1 (3) : 341-359. doi: 10.3934/naco.2011.1.341
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