1. An extragradient method for solving split feasibility and fixed point problems
- Author
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Ceng, L.-C., Ansari, Q.H., and Yao, J.-C.
- Subjects
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CONJUGATE gradient methods , *FEASIBILITY studies , *SPLITTING extrapolation method , *FIXED point theory , *HILBERT space , *NONEXPANSIVE mappings , *ALGORITHMS , *STOCHASTIC convergence - Abstract
Abstract: The purpose of this paper is to introduce and analyze an extragradient method with regularization for finding a common element of the solution set of the split feasibility problem and the set of fixed points of a nonexpansive mapping in the setting of infinite-dimensional Hilbert spaces. Combining the regularization method and the extragradient method due to Nadezhkina and Takahashi [N. Nadezhkina, W. Takahashi, Weak convergence theorem by an extragradient method for nonexpansive mappings and monotone mappings, J. Optim. Theory Appl. 128 (2006) 191–201], we propose an iterative algorithm for finding an element of . We prove that the sequences generated by the proposed algorithm converge weakly to an element of under mild conditions. [Copyright &y& Elsevier]
- Published
- 2012
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