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Global optimization of nonconvex problems with convex-transformable intermediates

Author

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  • Carlos J. Nohra

    (Carnegie Mellon University)

  • Nikolaos V. Sahinidis

    (Carnegie Mellon University)

Abstract

This paper addresses the global optimization of problems which contain convex-transformable functions. We present algorithms for identification of convex-transformable functions in general nonconvex problems, and introduce a new class of cutting planes based on recently developed relaxations for convex-transformable functions. These cutting planes correspond to the supporting hyperplanes of these convex relaxations. We integrate our recognition and cutting plane generation algorithms into the global solver BARON, and test our implementation by conducting numerical experiments on a large collection of nonconvex problems. Results demonstrate that the proposed implementation accelerates the convergence speed of the branch-and-bound algorithm, by significantly reducing computational time, number of nodes in the search tree, and required memory.

Suggested Citation

  • Carlos J. Nohra & Nikolaos V. Sahinidis, 2018. "Global optimization of nonconvex problems with convex-transformable intermediates," Journal of Global Optimization, Springer, vol. 72(2), pages 255-276, October.
    • Handle: RePEc:spr:jglopt:v:72:y:2018:i:2:d:10.1007_s10898-018-0631-4
    DOI: 10.1007/s10898-018-0631-4
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    References listed on IDEAS

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    1. Faiz A. Al-Khayyal & James E. Falk, 1983. "Jointly Constrained Biconvex Programming," Mathematics of Operations Research, INFORMS, vol. 8(2), pages 273-286, May.
    2. Hao-Chun Lu & Han-Lin Li & Chrysanthos Gounaris & Christodoulos Floudas, 2010. "Convex relaxation for solving posynomial programs," Journal of Global Optimization, Springer, vol. 46(1), pages 147-154, January.
    3. Ruth Misener & Christodoulos Floudas, 2014. "ANTIGONE: Algorithms for coNTinuous / Integer Global Optimization of Nonlinear Equations," Journal of Global Optimization, Springer, vol. 59(2), pages 503-526, July.
    4. Michael R. Bussieck & Arne Stolbjerg Drud & Alexander Meeraus, 2003. "MINLPLib—A Collection of Test Models for Mixed-Integer Nonlinear Programming," INFORMS Journal on Computing, INFORMS, vol. 15(1), pages 114-119, February.
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    Cited by:

    1. Aldrighetti, Riccardo & Battini, Daria & Ivanov, Dmitry, 2023. "Efficient resilience portfolio design in the supply chain with consideration of preparedness and recovery investments," Omega, Elsevier, vol. 117(C).

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