Artikel
Solving mixed-integer nonlinear optimization problems using simultaneous convexification: a case study for gas networks
Solving mixed-integer nonlinear optimization problems (MINLPs) to global optimality is extremely challenging. An important step for enabling their solution consists in the design of convex relaxations of the feasible set. Known solution approaches based on spatial branch-and-bound become more effective the tighter the used relaxations are. Relaxations are commonly established by convex underestimators, where each constraint function is considered separately. Instead, a considerably tighter relaxation can be found via so-called simultaneous convexification, where convex underestimators are derived for more than one constraint function at a time. In this work, we present a global solution approach for solving mixed-integer nonlinear problems that uses simultaneous convexification. We introduce a separation method that relies on determining the convex envelope of linear combinations of the constraint functions and on solving a nonsmooth convex problem. In particular, we apply the method to quadratic absolute value functions and derive their convex envelopes. The practicality of the proposed solution approach is demonstrated on several test instances from gas network optimization, where the method outperforms standard approaches that use separate convex relaxations.
- Language
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Englisch
- Bibliographic citation
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Journal: Journal of Global Optimization ; ISSN: 1573-2916 ; Volume: 80 ; Year: 2021 ; Issue: 2 ; Pages: 307-340 ; New York, NY: Springer US
- Classification
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Mathematik
- Subject
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Mixed-integer nonlinear programming
Simultaneous convexification
Convex envelope
Gas network optimization
- Event
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Geistige Schöpfung
- (who)
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Liers, Frauke
Martin, Alexander
Merkert, Maximilian
Mertens, Nick
Michaels, Dennis
- 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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2021
- DOI
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doi:10.1007/s10898-020-00974-0
- Last update
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10.03.2025, 11:44 AM CET
Data provider
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
- Liers, Frauke
- Martin, Alexander
- Merkert, Maximilian
- Mertens, Nick
- Michaels, Dennis
- Springer US
Time of origin
- 2021
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