Improving a Lagrangian decomposition for the unconstrained binary quadratic programming problem

This paper presents a new alternative of Lagrangian decomposition based on column generation technique to solve the unconstrained binary quadratic programming problem. We use a mixed binary linear version of the original quadratic problem with constraints represented by a graph. This graph is partit...

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Veröffentlicht in:Computers & operations research Jg. 39; H. 7; S. 1577 - 1581
Hauptverfasser: Mauri, Geraldo Regis, Lorena, Luiz Antonio Nogueira
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York Elsevier Ltd 01.07.2012
Elsevier
Pergamon Press Inc
Schlagworte:
Clusters
Column generation
Decomposition
Forming
Graph theory
Graphs
Lagrange multiplier
Lagrangian decomposition
Mathematical analysis
Mathematical models
Operations research
Quadratic programming
Studies
Quadratic programming
Lagrangian decomposition
Column generation
ISSN:0305-0548, 1873-765X, 0305-0548
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Abstract This paper presents a new alternative of Lagrangian decomposition based on column generation technique to solve the unconstrained binary quadratic programming problem. We use a mixed binary linear version of the original quadratic problem with constraints represented by a graph. This graph is partitioned into clusters of vertices forming subproblems whose solutions use the dual variables obtained by a coordinator problem. Computational experiments consider a set of difficult instances and the results are compared against other methods reported recently in the literature.
AbstractList This paper presents a new alternative of Lagrangian decomposition based on column generation technique to solve the unconstrained binary quadratic programming problem. We use a mixed binary linear version of the original quadratic problem with constraints represented by a graph. This graph is partitioned into clusters of vertices forming subproblems whose solutions use the dual variables obtained by a coordinator problem. Computational experiments consider a set of difficult instances and the results are compared against other methods reported recently in the literature. [PUBLICATION ABSTRACT]
This paper presents a new alternative of Lagrangian decomposition based on column generation technique to solve the unconstrained binary quadratic programming problem. We use a mixed binary linear version of the original quadratic problem with constraints represented by a graph. This graph is partitioned into clusters of vertices forming subproblems whose solutions use the dual variables obtained by a coordinator problem. Computational experiments consider a set of difficult instances and the results are compared against other methods reported recently in the literature.
Author Lorena, Luiz Antonio Nogueira
Mauri, Geraldo Regis
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  givenname: Luiz Antonio Nogueira
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CitedBy_id crossref_primary_10_1007_s10589_016_9844_y
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Cites_doi 10.1007/BF02247879
10.1007/s10589-005-3062-3
10.1111/j.1475-3995.2009.00743.x
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10.1006/jpdc.1997.1404
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Keywords Quadratic programming
Lagrangian decomposition
Column generation
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SubjectTerms Clusters
Column generation
Decomposition
Forming
Graph theory
Graphs
Lagrange multiplier
Lagrangian decomposition
Mathematical analysis
Mathematical models
Operations research
Quadratic programming
Studies
Title Improving a Lagrangian decomposition for the unconstrained binary quadratic programming problem
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