Título: | DECOMPOSITION AND RELAXATION ALGORITHMS FOR NONCONVEX MIXED INTEGER QUADRATICALLY CONSTRAINED QUADRATIC PROGRAMMING PROBLEMS | ||||||||||||
Autor: |
TIAGO COUTINHO CARNEIRO DE ANDRADE |
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Colaborador(es): |
SILVIO HAMACHER - Orientador FABRICIO CARLOS PINHEIRO OLIVEIRA - Coorientador |
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Catalogação: | 29/ABR/2019 | Língua(s): | ENGLISH - UNITED STATES |
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Tipo: | TEXT | Subtipo: | THESIS | ||||||||||
Notas: |
[pt] Todos os dados constantes dos documentos são de inteira responsabilidade de seus autores. Os dados utilizados nas descrições dos documentos estão em conformidade com os sistemas da administração da PUC-Rio. [en] All data contained in the documents are the sole responsibility of the authors. The data used in the descriptions of the documents are in conformity with the systems of the administration of PUC-Rio. |
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Referência(s): |
[pt] https://www.maxwell.vrac.puc-rio.br/projetosEspeciais/ETDs/consultas/conteudo.php?strSecao=resultado&nrSeq=37845&idi=1 [en] https://www.maxwell.vrac.puc-rio.br/projetosEspeciais/ETDs/consultas/conteudo.php?strSecao=resultado&nrSeq=37845&idi=2 |
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DOI: | https://doi.org/10.17771/PUCRio.acad.37845 | ||||||||||||
Resumo: | |||||||||||||
This thesis investigates and develops algorithms based on Lagrangian
relaxation and normalized multiparametric disaggregation technique
to solve nonconvex mixed-integer quadratically constrained quadratic programming.
First, relaxations for quadratic programming and related problem
classes are reviewed. Then, the normalized multiparametric disaggregation
technique is improved to a reformulated version, in which the size of
the generated subproblems are reduced in the number of binary variables.
Furthermore, issues related to the use of the Lagrangian relaxation to solve
nonconvex problems are addressed by replacing the dual subproblems with
convex relaxations. This method is compared to commercial and open source
off-the-shelf global solvers using randomly generated instances. The proposed
method converged in 35 of 36 instances, while Baron, the benchmark
solver that obtained the best results only converged in 4 of 36. Additionally,
even for the one instance the methods did not converge, it achieved relative
gaps below 1 percent in all instances, while Baron achieved relative gaps between
10 percent and 30 percent in most of them.
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