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On the relation between the extended supporting hyperplane algorithm and Kelley’s cutting plane algorithm (2020)

Serrano, Felipe ; Schwarz, Robert ; Gleixner, Ambros

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Publikationsdatum: 2021-02-06

Beschreibung: 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.

Sprache: Englisch

Materialart: article , doc-type:article

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