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Erscheinungsjahr: 
2020
Quellenangabe: 
[Journal:] Journal of Global Optimization [ISSN:] 1573-2916 [Volume:] 78 [Issue:] 1 [Publisher:] Springer US [Place:] New York, NY [Year:] 2020 [Pages:] 161-179
Verlag: 
Springer US, New York, NY
Zusammenfassung: 
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.
Schlagwörter: 
Convex MINLP
Cutting plane algorithms
Supporting hyperplane algorithm
Nonsmooth Optimization
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