Enhancements of discretization approaches for non-convex mixed-integer quadratically constrained quadratic programming: Part II
This is Part II of a study on mixed-integer programming (MIP) relaxation techniques for the solution of non-convex mixed-integer quadratically constrained quadratic programs (MIQCQPs). We set the focus on MIP relaxation methods for non-convex continuous variable products where both variables are bou...
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| Vydané v: | Computational optimization and applications Ročník 87; číslo 3; s. 893 - 934 |
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| Hlavní autori: | , , , , |
| Médium: | Journal Article |
| Jazyk: | English |
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New York, NY
Springer US
01.04.2024
Springer Nature B.V |
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| ISSN: | 1573-2894, 0926-6003, 1573-2894 |
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| Abstract | This is Part II of a study on mixed-integer programming (MIP) relaxation techniques for the solution of non-convex mixed-integer quadratically constrained quadratic programs (MIQCQPs). We set the focus on MIP relaxation methods for non-convex continuous variable products where both variables are bounded and extend the well-known MIP relaxation normalized multiparametric disaggregation technique (NMDT), applying a sophisticated discretization to both variables. We refer to this approach as doubly discretized normalized multiparametric disaggregation technique (D-NMDT). In a comprehensive theoretical analysis, we underline the theoretical advantages of the enhanced method D-NMDT compared to NMDT. Furthermore, we perform a broad computational study to demonstrate its effectiveness in terms of producing tight dual bounds for MIQCQPs. Finally, we compare D-NMDT to the separable MIP relaxations from Part I and a state-of-the-art MIQCQP solver. |
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| AbstractList | This is Part II of a study on mixed-integer programming (MIP) relaxation techniques for the solution of non-convex mixed-integer quadratically constrained quadratic programs (MIQCQPs). We set the focus on MIP relaxation methods for non-convex continuous variable products where both variables are bounded and extend the well-known MIP relaxation
normalized multiparametric disaggregation technique
(NMDT), applying a sophisticated discretization to both variables. We refer to this approach as
doubly discretized normalized multiparametric disaggregation technique
(D-NMDT). In a comprehensive theoretical analysis, we underline the theoretical advantages of the enhanced method D-NMDT compared to NMDT. Furthermore, we perform a broad computational study to demonstrate its effectiveness in terms of producing tight dual bounds for MIQCQPs. Finally, we compare D-NMDT to the separable MIP relaxations from Part I and a state-of-the-art MIQCQP solver. This is Part II of a study on mixed-integer programming (MIP) relaxation techniques for the solution of non-convex mixed-integer quadratically constrained quadratic programs (MIQCQPs). We set the focus on MIP relaxation methods for non-convex continuous variable products where both variables are bounded and extend the well-known MIP relaxation normalized multiparametric disaggregation technique (NMDT), applying a sophisticated discretization to both variables. We refer to this approach as doubly discretized normalized multiparametric disaggregation technique (D-NMDT). In a comprehensive theoretical analysis, we underline the theoretical advantages of the enhanced method D-NMDT compared to NMDT. Furthermore, we perform a broad computational study to demonstrate its effectiveness in terms of producing tight dual bounds for MIQCQPs. Finally, we compare D-NMDT to the separable MIP relaxations from Part I and a state-of-the-art MIQCQP solver. |
| Author | Hildebrand, Robert Bärmann, Andreas Beach, Benjamin Burlacu, Robert Hager, Lukas |
| Author_xml | – sequence: 1 givenname: Benjamin surname: Beach fullname: Beach, Benjamin – sequence: 2 givenname: Robert surname: Burlacu fullname: Burlacu, Robert – sequence: 3 givenname: Andreas surname: Bärmann fullname: Bärmann, Andreas – sequence: 4 givenname: Lukas surname: Hager fullname: Hager, Lukas – sequence: 5 givenname: Robert surname: Hildebrand fullname: Hildebrand, Robert |
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| Cites_doi | 10.1007/s101070100263 10.1007/s12532-018-0147-4 10.1016/j.neunet.2017.07.002 10.1287/ijoc.2023.1270 10.1080/10556788.2018.1556661 10.1007/BF01580665 10.1007/s10898-015-0342-z 10.1007/s12532-011-0033-9 10.1016/j.compchemeng.2020.106839 10.5334/jors.81 10.1007/s10107-005-0582-7 10.1007/s10898-022-01184-6 |
| ContentType | Journal Article |
| Copyright | The Author(s) 2024 The Author(s) 2024. This work is published under http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. |
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| DOI | 10.1007/s10589-024-00554-y |
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| References | Aigner, Burlacu, Liers, Martin (CR1) 2023; 35 CR3 Castro (CR7) 2015; 64 CR5 CR19 Yarotsky (CR20) 2017; 94 Bärmann, Burlacu, Hager, Kleinert (CR2) 2022; 1–31 CR18 CR9 CR14 Dolan, Moré (CR10) 2002; 91 CR13 CR11 Beach, Hildebrand, Ellis, Lebreton (CR4) 2020; 141 Siqueira, da Silva, Santos (CR17) 2016; 4 Furini, Traversi, Belotti, Frangioni, Gleixner, Gould, Liberti, Lodi, Misener, Mittelmann (CR12) 2019; 11 Chen, Burer (CR8) 2012; 4 Linderoth (CR15) 2005; 103 Burlacu, Geißler, Schewe (CR6) 2020; 35 McCormick (CR16) 1976; 10 554_CR13 554_CR14 554_CR11 J Chen (554_CR8) 2012; 4 ED Dolan (554_CR10) 2002; 91 F Furini (554_CR12) 2019; 11 R Burlacu (554_CR6) 2020; 35 B Beach (554_CR4) 2020; 141 J Linderoth (554_CR15) 2005; 103 GP McCormick (554_CR16) 1976; 10 K-M Aigner (554_CR1) 2023; 35 PM Castro (554_CR7) 2015; 64 554_CR9 AS Siqueira (554_CR17) 2016; 4 554_CR19 554_CR3 A Bärmann (554_CR2) 2022; 1–31 D Yarotsky (554_CR20) 2017; 94 554_CR5 554_CR18 |
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| SubjectTerms | Binarization Continuity (mathematics) Convex and Discrete Geometry Discretization Integer programming Linear programming Management Science Mathematics Mathematics and Statistics MIP Relaxations Mixed integer Operations Research Operations Research/Decision Theory Optimization Piecewise linear approximation Quadratic programming Statistics Variables |
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