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

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 poi...

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Bibliographic Details
Published inTaiwanese journal of mathematics Vol. 17; no. 3; pp. 911 - 936
Main Authors Ceng, L. C., Chou, C. Y.
Format Journal Article
LanguageEnglish
Published Mathematical Society of the Republic of China 01.06.2013
Subjects
Academic education
Algorithms
Hilbert spaces
Lipschitz condition
Mathematical monotonicity
Mathematical sets
Perceptron convergence procedure
Variational inequalities
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Summary: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 hybridextragradient 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. 2010Mathematics Subject Classification: 49J40, 65K05, 47H09. Key words and phrases: Constrained convex minimization, Variational inclusion, Variational inequality, Nonexpansive mapping, Inverse strongly monotone mapping, Maximal monotone mapping, Strong convergence.
ISSN:1027-5487
2224-6851
DOI:10.11650/tjm.17.2013.2567