Hybrid methods with regularization for minimization problems and asymptotically strict pseudocontractive mappings in the intermediate sense

Lu-Chuan Ceng (), Sy-Ming Guu () and Jen-Chih Yao ()

Journal of Global Optimization, 2014, vol. 60, issue 4, 617-634

Abstract: In this paper we introduce an iterative algorithm for finding a common element of the fixed point set of an asymptotically strict pseudocontractive mapping S in the intermediate sense and the solution set of the minimization problem (MP) for a convex and continuously Frechet differentiable functional in Hilbert space. The iterative algorithm is based on several well-known methods including the extragradient method, CQ method, Mann-type iterative method and hybrid gradient projection algorithm with regularization. We obtain a strong convergence theorem for three sequences generated by our iterative algorithm. In addition, we also prove a new weak convergence theorem by a modified extragradient method with regularization for the MP and the mapping S. Copyright Springer Science+Business Media New York 2014

Keywords: Extragradient method; Mann-type CQ method; Hybrid gradient projection algorithm with regularization; Minimization problem; Asymptotically strict pseudocontractive mapping in the intermediate sense; 49J30; 47H09; 47J20 (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/s10898-013-0087-5

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