7370
2019
eng
article
0
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On the Relation between the Extended Supporting Hyperplane Algorithm and Kelleyâ€™s Cutting Plane Algorithm
Recently, Kronqvist et al. (2016) rediscovered the supporting hyperplane algorithm of Veinott (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 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.
yes
under review
urn:nbn:de:0297-zib-73253
Felipe Serrano
Felipe Serrano
Robert Schwarz
Ambros Gleixner
Mathematical Optimization
Mathematical Optimization Methods
Gleixner, Ambros
Serrano, Felipe
MODAL-SynLab
MODAL-Gesamt
Schwarz, Robert
EnBA-M