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On the relation between the extended supporting hyperplane algorithm and Kelley’s cutting plane algorithm

Author

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  • Felipe Serrano

    (Zuse Institute Berlin)

  • Robert Schwarz

    (Zuse Institute Berlin)

  • Ambros Gleixner

    (Zuse Institute Berlin)

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.

Suggested Citation

  • Felipe Serrano & Robert Schwarz & Ambros Gleixner, 2020. "On the relation between the extended supporting hyperplane algorithm and Kelley’s cutting plane algorithm," Journal of Global Optimization, Springer, vol. 78(1), pages 161-179, September.
    • Handle: RePEc:spr:jglopt:v:78:y:2020:i:1:d:10.1007_s10898-020-00906-y
    DOI: 10.1007/s10898-020-00906-y
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    References listed on IDEAS

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    1. Tapio Westerlund & Ville-Pekka Eronen & Marko M. Mäkelä, 2018. "On solving generalized convex MINLP problems using supporting hyperplane techniques," Journal of Global Optimization, Springer, vol. 71(4), pages 987-1011, August.
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    6. Hoang Tuy, 2016. "Convex Analysis and Global Optimization," Springer Optimization and Its Applications, Springer, edition 2, number 978-3-319-31484-6, September.
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