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2013 ON THE RELAXED HYBRID-EXTRAGRADIENT METHOD FOR SOLVING CONSTRAINED CONVEX MINIMIZATION PROBLEMS IN HILBERT SPACES
Lu-Chuan Ceng, Chun-Yen Chou
Taiwanese J. Math. 17(3): 911-936 (2013). DOI: 10.11650/tjm.17.2013.2567

Abstract

In 2006, Nadezhkina and Takahashi [N. Nadezhkina, W. Takahashi, Strong convergence theorem by a hybrid method for nonexpansive mappings and Lipschitz-continuous monotone mappings, SIAM J. Optim., 16(4) (2006), 1230-1241.] introduced an iterative algorithm for finding a common element of the fixed point set of a nonexpansive mapping and the solution set of a variational inequality in a real Hilbert space via combining two well-known methods: hybrid and extragradient. In this paper, motivated by Nadezhkina and Takahashi's hybrid-extragradient method we propose and analyze a relaxed hybrid-extragradient method for finding a solution of a constrained convex minimization problem, which is also a common element of the solution set of a variational inclusion and the fixed point set of a strictly pseudocontractive mapping in a real Hilbert space. We obtain a strong convergence theorem for three sequences generated by this algorithm. Based on this result, we also construct an iterative algorithm for finding a solution of the constrained convex minimization problem, which is also a common fixed point of two mappings taken from the more general class of strictly pseudocontractive mappings.

Citation

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Lu-Chuan Ceng. Chun-Yen Chou. "ON THE RELAXED HYBRID-EXTRAGRADIENT METHOD FOR SOLVING CONSTRAINED CONVEX MINIMIZATION PROBLEMS IN HILBERT SPACES." Taiwanese J. Math. 17 (3) 911 - 936, 2013. https://doi.org/10.11650/tjm.17.2013.2567

Information

Published: 2013
First available in Project Euclid: 10 July 2017

zbMATH: 1280.49024
MathSciNet: MR3072269
Digital Object Identifier: 10.11650/tjm.17.2013.2567

Subjects:
Primary: 47H09 , 49J40 , 65K05

Keywords: constrained convex minimization , inverse strongly monotone mapping , maximal monotone mapping , Nonexpansive mapping , strong convergence , variational inclusion , variational inequality

Rights: Copyright © 2013 The Mathematical Society of the Republic of China

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Vol.17 • No. 3 • 2013
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