A unified hybrid iterative method for hierarchical minimization problems

In this paper, we introduce and analyze a new unified hybrid iterative method to compute the approximate solution of the general optimization problem defined over the set D=Fix(T)∩Ω[GMEP(Φ,Ψ,φ)], where Fix(T) is the set of common fixed points of a family T={T(t):0≤t<∞} of nonexpansive self-mappin...

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Bibliographic Details
Published in:Journal of computational and applied mathematics Vol. 253; pp. 208 - 221
Main Authors: Sahu, D.R., Ansari, Q.H., Yao, J.C.
Format: Journal Article
Language:English
Published: Elsevier B.V 01.12.2013
Subjects:
Hierarchical minimization problems
Hybrid iterative method
Maximal monotone operators
Metric projection mappings
Proximal point algorithm
Resolvent operators
Hybrid iterative method
47J20
Maximal monotone operators
Hierarchical minimization problems
49J40
Metric projection mappings
Resolvent operators
Proximal point algorithm
65J15
ISSN:0377-0427, 1879-1778
Online Access:Get full text
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Summary:In this paper, we introduce and analyze a new unified hybrid iterative method to compute the approximate solution of the general optimization problem defined over the set D=Fix(T)∩Ω[GMEP(Φ,Ψ,φ)], where Fix(T) is the set of common fixed points of a family T={T(t):0≤t<∞} of nonexpansive self-mappings on a Hilbert space H, and Ω[GMEP(Φ,Ψ,φ)] is the set of solutions of the generalized mixed equilibrium problem (in short, GMEP). Such type of minimization problem is called the hierarchical minimization problem. We establish the strong convergence of the sequences generated by the proposed algorithm. Our strong convergence theorem extends, improves and unifies the previously known results in the literature. We also give a numerical example to illustrate our algorithm and results.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2013.04.018