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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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
Online AccessGet full text
ISSN1027-5487
2224-6851
DOI10.11650/tjm.17.2013.2864

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Abstract 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.
AbstractList 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.
Author Ceng, Lu-Chuan
Wen, Ching-Feng
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SubjectTerms Algorithms
Coefficients
Hilbert spaces
Inner products
Mathematical constants
Mathematical monotonicity
Variational inequalities
Title HYBRID STEEPEST-DESCENT METHODS FOR TRIPLE HIERARCHICAL VARIATIONAL INEQUALITIES
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Volume 17
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