Artikel
On the relation between the extended supporting hyperplane algorithm and Kelley’s cutting plane algorithm
Recently, Kronqvist et al. (J Global Optim 64(2):249–272, 2016) rediscovered the supporting hyperplane algorithm of Veinott (Oper Res 15(1):147–152, 1967) and demonstrated its computational benefits for solving convex mixed integer nonlinear programs. In this paper we derive the algorithm from a geometric point of view. This enables us to show that the supporting hyperplane algorithm is equivalent to Kelley’s cutting plane algorithm (J Soc Ind Appl Math 8(4):703–712, 1960) applied to a particular reformulation of the problem. As a result, we extend the applicability of the supporting hyperplane algorithm to convex problems represented by a class of general, not necessarily convex nor differentiable, functions.
- Language
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Englisch
- Bibliographic citation
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Journal: Journal of Global Optimization ; ISSN: 1573-2916 ; Volume: 78 ; Year: 2020 ; Issue: 1 ; Pages: 161-179 ; New York, NY: Springer US
- Classification
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Mathematik
- Subject
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Convex MINLP
Cutting plane algorithms
Supporting hyperplane algorithm
Nonsmooth Optimization
- Event
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Geistige Schöpfung
- (who)
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Serrano, Felipe
Schwarz, Robert
Gleixner, Ambros
- Event
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Veröffentlichung
- (who)
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Springer US
- (where)
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New York, NY
- (when)
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2020
- DOI
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doi:10.1007/s10898-020-00906-y
- Last update
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10.03.2025, 11:45 AM CET
Data provider
This object is provided by:
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ZBW - Deutsche Zentralbibliothek für Wirtschaftswissenschaften - Leibniz-Informationszentrum Wirtschaft. If you have any questions about the object, please contact the data provider.
Object type
- Artikel
Associated
- Serrano, Felipe
- Schwarz, Robert
- Gleixner, Ambros
- Springer US
Time of origin
- 2020
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