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On the Relation between the Extended Supporting Hyperplane Algorithm and Kelley's Cutting Plane Algorithm

Felipe Serrano(serrano***at***zib.de)
Robert Schwarz(schwarz***at***zib.de)
Ambros Gleixner(gleixner***at***zib.de)

Abstract: Recently, Kronqvist et al.rediscovered the supporting hyperplane algorithm of Veinott 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 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 general, not necessarily convex, differentiable functions that satisfy a mild condition.

Keywords: Convex MINLP, Cutting plane algorithms, Supporting hyperplane algorithm

Category 1: Integer Programming ((Mixed) Integer Nonlinear Programming )

Category 2: Convex and Nonsmooth Optimization (Convex Optimization )

Citation: ZIB Report 19-18, Zuse Institute Berlin

Download: [PDF]

Entry Submitted: 05/20/2019
Entry Accepted: 05/20/2019
Entry Last Modified: 05/20/2019

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