Semidefinite programming lower bounds and branch-and-bound algorithms for the quadratic minimum spanning tree problem

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MetadadosDescriçãoIdioma
Autor(es): dc.creatorGuimarães, Dilson Almeida-
Autor(es): dc.creatorCunha, Alexandre Salles da-
Autor(es): dc.creatorPereira, Dilson Lucas-
Data de aceite: dc.date.accessioned2026-02-09T11:40:12Z-
Data de disponibilização: dc.date.available2026-02-09T11:40:12Z-
Data de envio: dc.date.issued2020-04-06-
Data de envio: dc.date.issued2020-04-06-
Data de envio: dc.date.issued2019-12-
Fonte completa do material: dc.identifierhttps://repositorio.ufla.br/handle/1/39813-
Fonte completa do material: dc.identifierhttps://www.sciencedirect.com/science/article/pii/S0377221719306022-
Fonte: dc.identifier.urihttp://educapes.capes.gov.br/handle/capes/1144805-
Descrição: dc.descriptionIn this paper, we investigate Semidefinite Programming (SDP) lower bounds for the Quadratic Minimum Spanning Tree Problem (QMSTP). Two SDP lower bounding approaches are introduced here. Both apply Lagrangian Relaxation to an SDP relaxation for the problem. The first one explicitly dualizes the semidefiniteness constraint, attaching to it a positive semidefinite matrix of Lagrangian multipliers. The second relies on a semi-infinite reformulation for the cone of positive semidefinite matrices and dualizes a dynamically updated finite set of inequalities that approximate the cone. These lower bounding procedures are the core ingredient of two QMSTP Branch-and-bound algorithms. Our computational experiments indicate that the SDP bounds computed here are very strong, being able to close at least 70% of the gaps of the most competitive formulation in the literature. As a result, their accompanying Branch-and-bound algorithms are competitive with the best previously available QMSTP exact algorithm in the literature. In fact, one of these new Branch-and-bound algorithms stands out as the new best exact solution approach for the problem.-
Idioma: dc.languageen-
Publicador: dc.publisherElsevier-
Direitos: dc.rightsrestrictAccess-
???dc.source???: dc.sourceEuropean Journal of Operational Research-
Palavras-chave: dc.subjectCombinatorial optimization-
Palavras-chave: dc.subjectSpanning trees-
Palavras-chave: dc.subjectLagrangian relaxation-
Palavras-chave: dc.subjectSemidefinite programming-
Palavras-chave: dc.subjectSemi-infinite programming-
Título: dc.titleSemidefinite programming lower bounds and branch-and-bound algorithms for the quadratic minimum spanning tree problem-
Tipo de arquivo: dc.typeArtigo-
Aparece nas coleções:Repositório Institucional da Universidade Federal de Lavras (RIUFLA)

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