Hybrid methods with regularization for minimization problems and asymptotically strict pseudocontractive mappings in the intermediate sense
By Lu-Chuan Ceng, Sy-Ming Guu, Jen-Chih Yao. Journal of Global Optimization, 2009
60 citations recorded by the source corpus.
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.
Subfields: Computational Theory and Mathematics, Geometry and Topology, Numerical Analysis
View Paper: https://www.semanticscholar.org/paper/57da4f7d8cc5f2db8de9dab69b8885c20e790f76
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In Computational Theory and Mathematics
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Citations in the corpus
- Asymptotically kn Strict Pseudocontractive Mappings in the Intermediate Sense (2011, background): “Hong-Kun Xu, Jen-Chih Yao [ 1 ] introduced the concept”