@article{SerranoSchwarzGleixner, 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}, series = {Journal of Global Optimization}, volume = {78}, journal = {Journal of Global Optimization}, doi = {10.1007/s10898-020-00906-y}, pages = {161 -- 179}, 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} }