Strong convergence of relaxed hybrid steepest-descent methods for triple hierarchical constrained optimization

Up to now, a large number of practical problems such as signal processing and network resource allocation have been formulated as the monotone variational inequality over the fixed point set of a nonexpansive mapping, and iterative algorithms for solving these problems have been proposed. The purpos...

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Published inFixed point theory and algorithms for sciences and engineering Vol. 2012; no. 1; pp. 1 - 24
Main Authors Zeng, L C, Wong, M M, Yao, J C
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 27.02.2012
Springer Nature B.V
BioMed Central Ltd
Subjects
Algorithms
Analysis
Applications of Mathematics
Constraints
Convergence
Differential Geometry
Inequalities
Mapping
Mathematical and Computational Biology
Mathematics
Mathematics and Statistics
Networks
Optimization
Resource allocation
Topology
relaxed hybrid steepest-descent method
fixed point
nonexpansive mapping
variational inequality
strong convergence
triple-hierarchical constrained optimization
monotone operator
Online AccessGet full text
ISSN1687-1812
1687-1820
1687-1812
2730-5422
DOI10.1186/1687-1812-2012-29

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Abstract Up to now, a large number of practical problems such as signal processing and network resource allocation have been formulated as the monotone variational inequality over the fixed point set of a nonexpansive mapping, and iterative algorithms for solving these problems have been proposed. The purpose of this article is to investigate a monotone variational inequality with variational inequality constraint over the fixed point set of one or finitely many nonexpansive mappings, which is called the triple-hierarchical constrained optimization. Two relaxed hybrid steepest-descent algorithms for solving the triple-hierarchical constrained optimization are proposed. Strong convergence for them is proven. Applications of these results to constrained generalized pseudoinverse are included. AMS Subject Classifications : 49J40; 65K05; 47H09.
AbstractList Up to now, a large number of practical problems such as signal processing and network resource allocation have been formulated as the monotone variational inequality over the fixed point set of a nonexpansive mapping, and iterative algorithms for solving these problems have been proposed. The purpose of this article is to investigate a monotone variational inequality with variational inequality constraint over the fixed point set of one or finitely many nonexpansive mappings, which is called the triple-hierarchical constrained optimization. Two relaxed hybrid steepest-descent algorithms for solving the triple-hierarchical constrained optimization are proposed. Strong convergence for them is proven. Applications of these results to constrained generalized pseudoinverse are included. AMS Subject Classifications : 49J40; 65K05; 47H09.
Up to now, a large number of practical problems such as signal processing and network resource allocation have been formulated as the monotone variational inequality over the fixed point set of a nonexpansive mapping, and iterative algorithms for solving these problems have been proposed. The purpose of this article is to investigate a monotone variational inequality with variational inequality constraint over the fixed point set of one or finitely many nonexpansive mappings, which is called the triple-hierarchical constrained optimization. Two relaxed hybrid steepest-descent algorithms for solving the triple-hierarchical constrained optimization are proposed. Strong convergence for them is proven. Applications of these results to constrained generalized pseudoinverse are included.AMS Subject Classifications: 49J40; 65K05; 47H09.
Up to now, a large number of practical problems such as signal processing and network resource allocation have been formulated as the monotone variational inequality over the fixed point set of a nonexpansive mapping, and iterative algorithms for solving these problems have been proposed. The purpose of this article is to investigate a monotone variational inequality with variational inequality constraint over the fixed point set of one or finitely many nonexpansive mappings, which is called the triple-hierarchical constrained optimization. Two relaxed hybrid steepest-descent algorithms for solving the triple-hierarchical constrained optimization are proposed. Strong convergence for them is proven. Applications of these results to constrained generalized pseudoinverse are included. AMS Subject Classifications: 49J40; 65K05; 47H09.[PUBLICATION ABSTRACT]
ArticleNumber 29
Author Yao, J C
Zeng, L C
Wong, M M
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  surname: Yao
  fullname: Yao, J C
  organization: Center for General Education, Kaohsiung Medical University
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CitedBy_id crossref_primary_10_1080_02331934_2019_1703978
crossref_primary_10_1155_2015_980352
crossref_primary_10_1155_2014_767109
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ContentType Journal Article
Copyright Zeng et al.; licensee Springer. 2012. This article is published under license to BioMed Central Ltd. This is an open access article distributed under the terms of the Creative Commons Attribution License ( ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Springer International Publishing AG 2012
Copyright_xml – notice: Zeng et al.; licensee Springer. 2012. This article is published under license to BioMed Central Ltd. This is an open access article distributed under the terms of the Creative Commons Attribution License ( ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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Keywords relaxed hybrid steepest-descent method
fixed point
nonexpansive mapping
variational inequality
strong convergence
triple-hierarchical constrained optimization
monotone operator
Language English
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Snippet Up to now, a large number of practical problems such as signal processing and network resource allocation have been formulated as the monotone variational...
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SubjectTerms Algorithms
Analysis
Applications of Mathematics
Constraints
Convergence
Differential Geometry
Inequalities
Mapping
Mathematical and Computational Biology
Mathematics
Mathematics and Statistics
Networks
Optimization
Resource allocation
Topology
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Title Strong convergence of relaxed hybrid steepest-descent methods for triple hierarchical constrained optimization
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