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Zbl 1252.65102
Ceng, L.-C.; Ansari, Q.H.; Yao, J.-C.
An extragradient method for solving split feasibility and fixed point problems.
(English)
[J] Comput. Math. Appl. 64, No. 4, 633-642 (2012). ISSN 0898-1221

Summary: The purpose of this paper is to introduce and analyze an extragradient method with regularization for finding a common element of the solution set $\Gamma$ of the split feasibility problem and the set $\mathrm{Fix}(S)$ of fixed points of a nonexpansive mapping $S$ in the setting of infinite-dimensional Hilbert spaces. Combining the regularization method and the extragradient method due to {\it N. Nadezhkina} and {\it W. Takahashi} [J. Optim. Theory Appl. 128, No.~1, 191--201 (2006; Zbl 1130.90055)], we propose an iterative algorithm for finding an element of $\mathrm{Fix}(S)\cap \Gamma$. We prove that the sequences generated by the proposed algorithm converge weakly to an element of $\mathrm{Fix}(S)\cap \Gamma$ under mild conditions.
MSC 2000:
*65K10 Optimization techniques (numerical methods)
47J25 Methods for solving nonlinear operator equations (general)

Keywords: split feasibility problems; fixed point problems; extragradient method; regularization; averaged mappings; maximal monotone mappings

Citations: Zbl 1130.90055

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