HYBRID STEEPEST-DESCENT METHODS FOR TRIPLE HIERARCHICAL VARIATIONAL INEQUALITIES

In this paper, we consider a triple hierarchical variational inequality defined over the common solution set of minimization and mixed equilibrium problems. Combining the hybrid steepest-descent method, viscosity approximation method and averaged mapping approach to the gradient-projection algorithm...

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Bibliographic Details
Published inTaiwanese journal of mathematics Vol. 17; no. 4; pp. 1441 - 1472
Main Authors Ceng, Lu-Chuan, Wen, Ching-Feng
Format Journal Article
LanguageEnglish
Published Mathematical Society of the Republic of China 01.08.2013
Subjects
Algorithms
Coefficients
Hilbert spaces
Inner products
Mathematical constants
Mathematical monotonicity
Variational inequalities
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ISSN1027-5487
2224-6851
DOI10.11650/tjm.17.2013.2864

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Summary:In this paper, we consider a triple hierarchical variational inequality defined over the common solution set of minimization and mixed equilibrium problems. Combining the hybrid steepest-descent method, viscosity approximation method and averaged mapping approach to the gradient-projection algorithm, we propose two iterative methods: implicit one and explicit one, to compute the approximate solutions of our problem. The convergence analysis of the sequences generated by the proposed methods is also established. 2010Mathematics Subject Classification: 49J40, 47J20, 47H10, 65K05, 47H09. Key words and phrases: Triple hierarchical variational inequality, Minimization problem, Mixed equilibrium problem, Implicit iterative algorithm, Explicit iterative algorithm, Averaged mapping approach.
ISSN:1027-5487
2224-6851
DOI:10.11650/tjm.17.2013.2864