Enhancing the normalized multiparametric disaggregation technique for mixed-integer quadratic programming
We propose methods for improving the relaxations obtained by the normalized multiparametric disaggregation technique (NMDT). These relaxations constitute a key component for some methods for solving nonconvex mixed-integer quadratically constrained quadratic programming (MIQCQP) problems. It is show...
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| Vydané v: | Journal of global optimization Ročník 73; číslo 4; s. 701 - 722 |
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| Hlavní autori: | , , , |
| Médium: | Journal Article |
| Jazyk: | English |
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New York
Springer US
15.04.2019
Springer Springer Nature B.V |
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| ISSN: | 0925-5001, 1573-2916 |
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| Abstract | We propose methods for improving the relaxations obtained by the normalized multiparametric disaggregation technique (NMDT). These relaxations constitute a key component for some methods for solving nonconvex mixed-integer quadratically constrained quadratic programming (MIQCQP) problems. It is shown that these relaxations can be more efficiently formulated by significantly reducing the number of auxiliary variables (in particular, binary variables) and constraints. Moreover, a novel algorithm for solving MIQCQP problems is proposed. It can be applied using either its original NMDT or the proposed reformulation. Computational experiments are performed using both benchmark instances from the literature and randomly generated instances. The numerical results suggest that the proposed techniques can improve the quality of the relaxations. |
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| AbstractList | We propose methods for improving the relaxations obtained by the normalized multiparametric disaggregation technique (NMDT). These relaxations constitute a key component for some methods for solving nonconvex mixed-integer quadratically constrained quadratic programming (MIQCQP) problems. It is shown that these relaxations can be more efficiently formulated by significantly reducing the number of auxiliary variables (in particular, binary variables) and constraints. Moreover, a novel algorithm for solving MIQCQP problems is proposed. It can be applied using either its original NMDT or the proposed reformulation. Computational experiments are performed using both benchmark instances from the literature and randomly generated instances. The numerical results suggest that the proposed techniques can improve the quality of the relaxations. |
| Audience | Academic |
| Author | Eberhard, Andrew Oliveira, Fabricio Andrade, Tiago Hamacher, Silvio |
| Author_xml | – sequence: 1 givenname: Tiago surname: Andrade fullname: Andrade, Tiago organization: Pontifícia Universidade Católica do Rio de Janeiro (Puc-Rio) R. Marquês de São Vicente – sequence: 2 givenname: Fabricio orcidid: 0000-0003-0300-9337 surname: Oliveira fullname: Oliveira, Fabricio organization: Systems Analysis Laboratory, Department of Mathematics and Systems Analysis, School of Science, Aalto University – sequence: 3 givenname: Silvio surname: Hamacher fullname: Hamacher, Silvio organization: Pontifícia Universidade Católica do Rio de Janeiro (Puc-Rio) R. Marquês de São Vicente – sequence: 4 givenname: Andrew orcidid: 0000-0003-2977-3456 surname: Eberhard fullname: Eberhard, Andrew email: andy.eberhard@rmit.edu.au organization: RMIT University |
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| CitedBy_id | crossref_primary_10_1007_s10898_025_01491_8 crossref_primary_10_1016_j_compchemeng_2020_107205 crossref_primary_10_1016_j_compchemeng_2021_107459 crossref_primary_10_1016_j_compchemeng_2020_106883 crossref_primary_10_1007_s10898_022_01138_y crossref_primary_10_1007_s10589_022_00440_5 crossref_primary_10_1016_j_compchemeng_2023_108229 crossref_primary_10_1109_TSTE_2024_3422236 crossref_primary_10_1111_itor_70001 crossref_primary_10_1109_TCYB_2021_3088221 crossref_primary_10_1016_j_compchemeng_2023_108539 crossref_primary_10_1002_aic_17404 crossref_primary_10_1007_s11081_021_09603_5 |
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| Keywords | McCormick envelopes Convex relaxation Nonconvex mixed-integer quadratically constrained quadratic programs Normalized multiparametric disaggregation technique |
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| Title | Enhancing the normalized multiparametric disaggregation technique for mixed-integer quadratic programming |
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