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On the relation between the extended supporting hyperplane algorithm and Kelley’s cutting plane algorithm
Journal of Global Optimization ( IF 1.3 ) Pub Date : 2020-05-13 , DOI: 10.1007/s10898-020-00906-y
Felipe Serrano , Robert Schwarz , Ambros Gleixner

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.



中文翻译:

关于扩展支持超平面算法与凯利切平面算法之间的关系

最近,Kronqvist等人。(J Global Optim 64(2):249–272,2016)重新发现了Veinott的支持超平面算法(Oper Res 15(1):147–152,1967),并证明了其解决凸混合整数非线性程序的计算优势。在本文中,我们从几何角度推导了该算法。这使我们能够证明,支持超平面算法等同于凯利的切平面算法(J Soc Ind Appl Math 8(4):703–712,1960),适用于该问题的特定重构。结果,我们将支持超平面算法的适用性扩展到由一类通用函数表示的凸问题,这些函数不一定是凸函数,也不是可微函数。

更新日期:2020-05-13
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