On the Relation between the Extended Supporting Hyperplane Algorithm and Kelley’s Cutting Plane Algorithm
Please always quote using this URN: urn:nbn:de:0297-zib-73253
- 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.
| Author: | Felipe SerranoORCiD, Robert SchwarzORCiD, Ambros GleixnerORCiD |
|---|---|
| Document Type: | ZIB-Report |
| Date of first Publication: | 2019/05/20 |
| Series (Serial Number): | ZIB-Report (19-18) |
| ISSN: | 1438-0064 |
