@misc{SerranoSchwarzGleixner2019, author = {Serrano, Felipe and Schwarz, Robert and Gleixner, Ambros}, title = {On the Relation between the Extended Supporting Hyperplane Algorithm and Kelley's Cutting Plane Algorithm}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-73253}, year = {2019}, abstract = {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.}, language = {en} } @article{SerranoSchwarzGleixner2020, author = {Serrano, Felipe and Schwarz, Robert and Gleixner, Ambros}, title = {On the relation between the extended supporting hyperplane algorithm and Kelley's cutting plane algorithm}, volume = {78}, journal = {Journal of Global Optimization}, doi = {10.1007/s10898-020-00906-y}, pages = {161 -- 179}, year = {2020}, abstract = {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.}, language = {en} }