Academic Journal
Building Formulations for Piecewise Linear Relaxations of Nonlinear Functions.
| Title: | Building Formulations for Piecewise Linear Relaxations of Nonlinear Functions. |
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| Authors: | Lyu, Bochuan1 (AUTHOR) bochuan.lyu@gmail.com, Hicks, Illya V.1 (AUTHOR) ivhicks@rice.edu, Huchette, Joey2 (AUTHOR) jhuchette@google.com |
| Source: | Operations Research. Jan/Feb2026, Vol. 74 Issue 1, p484-499. 16p. |
| Subject Terms: | *Empirical research, Mixed integer linear programming, Nonlinear functions, Piecewise linear approximation, Mathematical bounds, Combinatorial optimization, Substructuring techniques |
| Abstract: | We study mixed-integer programming formulations for the piecewise linear lower and upper bounds (in other words, piecewise linear relaxations) of nonlinear functions that can be modeled by a new class of combinatorial disjunctive constraints (CDCs), generalized nD-ordered CDCs. We first introduce a general formulation technique to model piecewise linear lower and upper bounds of univariate nonlinear functions concurrently so that it uses fewer binary variables than modeling bounds separately. Next, we propose logarithmically sized ideal nonextended formulations to model the piecewise linear relaxations of univariate and higher-dimensional nonlinear functions under the CDC and independent branching frameworks. We also perform computational experiments for the approaches modeling the piecewise linear relaxations of nonlinear functions and show significant speed-ups of our proposed formulations. Furthermore, we demonstrate that piecewise linear relaxations can provide strong dual bounds of the original problems with less computational time by an order of magnitude. [ABSTRACT FROM AUTHOR] |
| Copyright of Operations Research 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.) | |
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| Items | – Name: Title Label: Title Group: Ti Data: Building Formulations for Piecewise Linear Relaxations of Nonlinear Functions. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Lyu%2C+Bochuan%22">Lyu, Bochuan</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> bochuan.lyu@gmail.com</i><br /><searchLink fieldCode="AR" term="%22Hicks%2C+Illya+V%2E%22">Hicks, Illya V.</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> ivhicks@rice.edu</i><br /><searchLink fieldCode="AR" term="%22Huchette%2C+Joey%22">Huchette, Joey</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> jhuchette@google.com</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Operations+Research%22">Operations Research</searchLink>. Jan/Feb2026, Vol. 74 Issue 1, p484-499. 16p. – Name: Subject Label: Subject Terms Group: Su Data: *<searchLink fieldCode="DE" term="%22Empirical+research%22">Empirical research</searchLink><br /><searchLink fieldCode="DE" term="%22Mixed+integer+linear+programming%22">Mixed integer linear programming</searchLink><br /><searchLink fieldCode="DE" term="%22Nonlinear+functions%22">Nonlinear functions</searchLink><br /><searchLink fieldCode="DE" term="%22Piecewise+linear+approximation%22">Piecewise linear approximation</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+bounds%22">Mathematical bounds</searchLink><br /><searchLink fieldCode="DE" term="%22Combinatorial+optimization%22">Combinatorial optimization</searchLink><br /><searchLink fieldCode="DE" term="%22Substructuring+techniques%22">Substructuring techniques</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: We study mixed-integer programming formulations for the piecewise linear lower and upper bounds (in other words, piecewise linear relaxations) of nonlinear functions that can be modeled by a new class of combinatorial disjunctive constraints (CDCs), generalized nD-ordered CDCs. We first introduce a general formulation technique to model piecewise linear lower and upper bounds of univariate nonlinear functions concurrently so that it uses fewer binary variables than modeling bounds separately. Next, we propose logarithmically sized ideal nonextended formulations to model the piecewise linear relaxations of univariate and higher-dimensional nonlinear functions under the CDC and independent branching frameworks. We also perform computational experiments for the approaches modeling the piecewise linear relaxations of nonlinear functions and show significant speed-ups of our proposed formulations. Furthermore, we demonstrate that piecewise linear relaxations can provide strong dual bounds of the original problems with less computational time by an order of magnitude. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Operations Research 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/opre.2023.0187 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 16 StartPage: 484 Subjects: – SubjectFull: Empirical research Type: general – SubjectFull: Mixed integer linear programming Type: general – SubjectFull: Nonlinear functions Type: general – SubjectFull: Piecewise linear approximation Type: general – SubjectFull: Mathematical bounds Type: general – SubjectFull: Combinatorial optimization Type: general – SubjectFull: Substructuring techniques Type: general Titles: – TitleFull: Building Formulations for Piecewise Linear Relaxations of Nonlinear Functions. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Lyu, Bochuan – PersonEntity: Name: NameFull: Hicks, Illya V. – PersonEntity: Name: NameFull: Huchette, Joey IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 01 Text: Jan/Feb2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 0030364X Numbering: – Type: volume Value: 74 – Type: issue Value: 1 Titles: – TitleFull: Operations Research Type: main |
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