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A new extragradient-type algorithm for the split feasibility problem. (English) Zbl 1400.90301

Summary: We consider the split feasibility problem (SFP) in Hilbert spaces, inspired by extragradient method presented by L. C. Ceng et al. [Comput. Math. Appl. 64, No. 4, 633–642 (2012; Zbl 1252.65102)] for split feasibility problem, subgradient extragradient method proposed by Y. Censor [Math. Program. 42, No. 2 (B), 307–325 (1988; Zbl 0658.90099)], and variant extragradient-type method presented by Y. Yao et al. [Fixed Point Theory Appl. 2013, Paper No. 185, 15 p. (2013; Zbl 1476.47085)] for variational inequalities; we suggest an extragradient-type algorithm for the SFP. We prove the strong convergence under some suitable conditions in infinite-dimensional Hilbert spaces.

MSC:

90C48 Programming in abstract spaces
65K05 Numerical mathematical programming methods
47J20 Variational and other types of inequalities involving nonlinear operators (general)
90C25 Convex programming
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