Taiwanese Journal of Mathematics

ON THE RELAXED HYBRID-EXTRAGRADIENT METHOD FOR SOLVING CONSTRAINED CONVEX MINIMIZATION PROBLEMS IN HILBERT SPACES

Lu-Chuan Ceng and Chun-Yen Chou

Full-text: Open access

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.

Article information

Source
Taiwanese J. Math., Volume 17, Number 3 (2013), 911-936.

Dates
First available in Project Euclid: 10 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1499705991

Digital Object Identifier
doi:10.11650/tjm.17.2013.2567

Mathematical Reviews number (MathSciNet)
MR3072269

Zentralblatt MATH identifier
1280.49024

Subjects
Primary: 49J40: Variational methods including variational inequalities [See also 47J20] 65K05: Mathematical programming methods [See also 90Cxx] 47H09: Contraction-type mappings, nonexpansive mappings, A-proper mappings, etc.

Keywords
constrained convex minimization variational inclusion variational inequality nonexpansive mapping inverse strongly monotone mapping maximal monotone mapping strong convergence

Citation

Ceng, Lu-Chuan; Chou, Chun-Yen. ON THE RELAXED HYBRID-EXTRAGRADIENT METHOD FOR SOLVING CONSTRAINED CONVEX MINIMIZATION PROBLEMS IN HILBERT SPACES. Taiwanese J. Math. 17 (2013), no. 3, 911--936. doi:10.11650/tjm.17.2013.2567. https://projecteuclid.org/euclid.twjm/1499705991


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