Academic Journal
Spatial Branch-and-Bound for Nonconvex Separable Piecewise Linear Optimization.
| Τίτλος: | Spatial Branch-and-Bound for Nonconvex Separable Piecewise Linear Optimization. |
|---|---|
| Συγγραφείς: | Hübner, Thomas, Gupte, Akshay, Rebennack, Steffen |
| Πηγή: | INFORMS Journal on Computing; Mar/Apr2026, Vol. 38 Issue 2, p645-675, 31p |
| Θεματικοί όροι: | Branch & bound algorithms, Piecewise linear approximation, Mathematical optimization, Convex functions, Knapsack problems, Global optimization, Mixed integer linear programming |
| Περίληψη: | Nonconvex separable piecewise linear functions (PLFs) frequently appear in applications and to approximate nonlinearitites. The standard practice to formulate nonconvex PLFs is from the perspective of discrete optimization using special ordered sets and mixed-integer linear programs (MILPs). In contrast, we take the viewpoint of global continuous optimization and present a spatial branch-and-bound algorithm for optimizing a separable discontinuous PLF over a closed convex set. It offers slim and sparse linear programming relaxations, sharpness throughout the search tree, and an increased flexibility in branching decisions. The main feature of our algorithm is the generation of convex underestimators at the root node of the search tree and their quick and efficient updates at each node after branching. Convergence to the global optimum is achieved when the PLFs are lower semicontinuous. A Python implementation of our algorithm is tested on knapsack and network flow problems for both continuous and discontinuous PLFs. Our algorithm is compared with four logarithmic MILP formulations solved by Gurobi's MILP solver as well as Gurobi's PLF solver. We also compare our method against mixed-integer nonlinear program formulations solved by Gurobi. The numerical experiments indicate significant performance gains up to two orders of magnitude for medium- to large-sized PLFs. Finally, we also give an upper bound on the additive error from PLF approximations of nonconvex separable optimization. History: Accepted by Andrea Lodi, Area Editor for Design & Analysis of Algorithms–Discrete. Funding: The research of S. Rebennack is supported by the Deutsche Forschungsgemeinschaft [Grant 445857709]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information (https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2024.0755) as well as from the IJOC GitHub software repository (https://github.com/INFORMSJoC/2024.0755). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/. [ABSTRACT FROM AUTHOR] |
| Copyright of INFORMS Journal on Computing is the property of INFORMS: Institute for Operations Research & the Management Sciences and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Βάση Δεδομένων: | Complementary Index |
| FullText | Text: Availability: 0 |
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| Header | DbId: edb DbLabel: Complementary Index An: 192991000 RelevancyScore: 1121 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 1121.07177734375 |
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| Items | – Name: Title Label: Title Group: Ti Data: Spatial Branch-and-Bound for Nonconvex Separable Piecewise Linear Optimization. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Hübner%2C+Thomas%22">Hübner, Thomas</searchLink><br /><searchLink fieldCode="AR" term="%22Gupte%2C+Akshay%22">Gupte, Akshay</searchLink><br /><searchLink fieldCode="AR" term="%22Rebennack%2C+Steffen%22">Rebennack, Steffen</searchLink> – Name: TitleSource Label: Source Group: Src Data: INFORMS Journal on Computing; Mar/Apr2026, Vol. 38 Issue 2, p645-675, 31p – Name: Subject Label: Subject Terms Group: Su Data: <searchLink fieldCode="DE" term="%22Branch+%26+bound+algorithms%22">Branch & bound algorithms</searchLink><br /><searchLink fieldCode="DE" term="%22Piecewise+linear+approximation%22">Piecewise linear approximation</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+optimization%22">Mathematical optimization</searchLink><br /><searchLink fieldCode="DE" term="%22Convex+functions%22">Convex functions</searchLink><br /><searchLink fieldCode="DE" term="%22Knapsack+problems%22">Knapsack problems</searchLink><br /><searchLink fieldCode="DE" term="%22Global+optimization%22">Global optimization</searchLink><br /><searchLink fieldCode="DE" term="%22Mixed+integer+linear+programming%22">Mixed integer linear programming</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: Nonconvex separable piecewise linear functions (PLFs) frequently appear in applications and to approximate nonlinearitites. The standard practice to formulate nonconvex PLFs is from the perspective of discrete optimization using special ordered sets and mixed-integer linear programs (MILPs). In contrast, we take the viewpoint of global continuous optimization and present a spatial branch-and-bound algorithm for optimizing a separable discontinuous PLF over a closed convex set. It offers slim and sparse linear programming relaxations, sharpness throughout the search tree, and an increased flexibility in branching decisions. The main feature of our algorithm is the generation of convex underestimators at the root node of the search tree and their quick and efficient updates at each node after branching. Convergence to the global optimum is achieved when the PLFs are lower semicontinuous. A Python implementation of our algorithm is tested on knapsack and network flow problems for both continuous and discontinuous PLFs. Our algorithm is compared with four logarithmic MILP formulations solved by Gurobi's MILP solver as well as Gurobi's PLF solver. We also compare our method against mixed-integer nonlinear program formulations solved by Gurobi. The numerical experiments indicate significant performance gains up to two orders of magnitude for medium- to large-sized PLFs. Finally, we also give an upper bound on the additive error from PLF approximations of nonconvex separable optimization. History: Accepted by Andrea Lodi, Area Editor for Design & Analysis of Algorithms–Discrete. Funding: The research of S. Rebennack is supported by the Deutsche Forschungsgemeinschaft [Grant 445857709]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information (https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2024.0755) as well as from the IJOC GitHub software repository (https://github.com/INFORMSJoC/2024.0755). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/. [ABSTRACT FROM AUTHOR] – Name: Abstract Label: Group: Ab Data: <i>Copyright of INFORMS Journal on Computing is the property of INFORMS: Institute for Operations Research & the Management Sciences and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1287/ijoc.2024.0755 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 31 StartPage: 645 Subjects: – SubjectFull: Branch & bound algorithms Type: general – SubjectFull: Piecewise linear approximation Type: general – SubjectFull: Mathematical optimization Type: general – SubjectFull: Convex functions Type: general – SubjectFull: Knapsack problems Type: general – SubjectFull: Global optimization Type: general – SubjectFull: Mixed integer linear programming Type: general Titles: – TitleFull: Spatial Branch-and-Bound for Nonconvex Separable Piecewise Linear Optimization. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Hübner, Thomas – PersonEntity: Name: NameFull: Gupte, Akshay – PersonEntity: Name: NameFull: Rebennack, Steffen IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 03 Text: Mar/Apr2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 10919856 Numbering: – Type: volume Value: 38 – Type: issue Value: 2 Titles: – TitleFull: INFORMS Journal on Computing Type: main |
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