Global optimization of general nonconvex problems with intermediate polynomial substructures
This work considers the global optimization of general nonconvex nonlinear and mixed-integer nonlinear programming problems with underlying polynomial substructures. We incorporate linear cutting planes inspired by reformulation-linearization techniques to produce tight subproblem formulations that...
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| Vydáno v: | Journal of global optimization Ročník 59; číslo 2-3; s. 673 - 693 |
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| Hlavní autoři: | , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
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Boston
Springer US
01.07.2014
Springer Springer Nature B.V |
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| ISSN: | 0925-5001, 1573-2916 |
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| Abstract | This work considers the global optimization of general nonconvex nonlinear and mixed-integer nonlinear programming problems with underlying polynomial substructures. We incorporate linear cutting planes inspired by reformulation-linearization techniques to produce tight subproblem formulations that exploit these underlying structures. These cutting plane strategies simultaneously convexify linear and nonlinear terms from multiple constraints and are highly effective at tightening standard linear programming relaxations generated by sequential factorable programming techniques. Because the number of available cutting planes increases exponentially with the number of variables, we implement cut filtering and selection strategies to prevent an exponential increase in relaxation size. We introduce algorithms for polynomial substructure detection, cutting plane identification, cut filtering, and cut selection and embed the proposed implementation in BARON at every node in the branch-and-bound tree. A computational study including randomly generated problems of varying size and complexity demonstrates that the exploitation of underlying polynomial substructures significantly reduces computational time, branch-and-bound tree size, and required memory. |
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| AbstractList | This work considers the global optimization of general nonconvex nonlinear and mixed-integer nonlinear programming problems with underlying polynomial substructures. We incorporate linear cutting planes inspired by reformulation-linearization techniques to produce tight subproblem formulations that exploit these underlying structures. These cutting plane strategies simultaneously convexify linear and nonlinear terms from multiple constraints and are highly effective at tightening standard linear programming relaxations generated by sequential factorable programming techniques. Because the number of available cutting planes increases exponentially with the number of variables, we implement cut filtering and selection strategies to prevent an exponential increase in relaxation size. We introduce algorithms for polynomial substructure detection, cutting plane identification, cut filtering, and cut selection and embed the proposed implementation in BARON at every node in the branch-and-bound tree. A computational study including randomly generated problems of varying size and complexity demonstrates that the exploitation of underlying polynomial substructures significantly reduces computational time, branch-and-bound tree size, and required memory. Issue Title: Special Issue: Honoring the 60th birthday of Panos M. Pardalos This work considers the global optimization of general nonconvex nonlinear and mixed-integer nonlinear programming problems with underlying polynomial substructures. We incorporate linear cutting planes inspired by reformulation-linearization techniques to produce tight subproblem formulations that exploit these underlying structures. These cutting plane strategies simultaneously convexify linear and nonlinear terms from multiple constraints and are highly effective at tightening standard linear programming relaxations generated by sequential factorable programming techniques. Because the number of available cutting planes increases exponentially with the number of variables, we implement cut filtering and selection strategies to prevent an exponential increase in relaxation size. We introduce algorithms for polynomial substructure detection, cutting plane identification, cut filtering, and cut selection and embed the proposed implementation in BARON at every node in the branch-and-bound tree. A computational study including randomly generated problems of varying size and complexity demonstrates that the exploitation of underlying polynomial substructures significantly reduces computational time, branch-and-bound tree size, and required memory.[PUBLICATION ABSTRACT] |
| Audience | Academic |
| Author | Sahinidis, Nikolaos V. Zorn, Keith |
| Author_xml | – sequence: 1 givenname: Keith surname: Zorn fullname: Zorn, Keith organization: Department of Chemical Engineering, Carnegie Mellon University – sequence: 2 givenname: Nikolaos V. surname: Sahinidis fullname: Sahinidis, Nikolaos V. email: sahinidis@cmu.edu organization: Department of Chemical Engineering, Carnegie Mellon University |
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| CitedBy_id | crossref_primary_10_1016_j_compchemeng_2016_02_013 crossref_primary_10_1007_s10589_024_00633_0 crossref_primary_10_1007_s12532_016_0099_5 crossref_primary_10_1016_j_compchemeng_2022_107909 crossref_primary_10_1016_j_ejor_2015_12_018 crossref_primary_10_1287_ijoc_2023_0390 crossref_primary_10_1080_10556788_2017_1350178 |
| Cites_doi | 10.1007/BF00138689 10.1007/s10898-011-9747-5 10.1287/moor.8.2.273 10.1023/B:JOGO.0000042112.72379.e6 10.1007/s10107-011-0496-5 10.1023/A:1009934614393 10.1080/14697681003756877 10.1007/s10898-010-9639-0 10.1007/s10898-005-2099-2 10.1007/s10107-005-0581-8 10.1016/S0167-6377(97)00013-8 10.1080/10556788.2013.783032 10.1287/opre.38.2.217 10.1137/050640308 10.1007/BF01580665 10.1007/BF00121304 10.1137/0403036 10.1007/s10107-003-0467-6 10.1007/BF00122429 10.1007/978-1-4757-3532-1 10.1007/PL00011409 10.1287/opre.50.2.358.424 10.1007/s10107-012-0618-8 10.1007/s10107-006-0040-1 10.1007/s10107-002-0308-z 10.1023/A:1008237515535 10.1007/BF01100203 10.1080/10556780902883184 10.1007/0-387-29550-X_16 10.1007/s10898-012-9874-7 10.1007/s10107-012-0581-4 10.1007/s12532-014-0073-z 10.1145/984622.984630 |
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| Keywords | Factorable polyhedral relaxation Reformulation-linearization techniques Branch-and-bound global optimization Polynomial programming |
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| SubjectTerms | Algorithms Branch & bound algorithms Computer Science Cutting Filtering Linear programming Mathematical analysis Mathematical models Mathematical programming Mathematics Mathematics and Statistics Operations Research/Decision Theory Optimization Planes Polynomials Real Functions Studies Substructures Variables |
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| Title | Global optimization of general nonconvex problems with intermediate polynomial substructures |
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