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On Solving Nonsmooth Mixed-Integer Nonlinear Programming Problems by Outer Approximation and Generalized Benders Decomposition

Author

Listed:
  • Zhou Wei

    (Yunnan University)

  • M. Montaz Ali

    (University of the Witwatersrand)

  • Liang Xu

    (University of Pittsburgh)

  • Bo Zeng

    (University of Pittsburgh)

  • Jen-Chih Yao

    (Zhejiang Normal University
    China Medical University)

Abstract

In this paper, we mainly study nonsmooth mixed-integer nonlinear programming problems and solution algorithms by outer approximation and generalized Benders decomposition. Outer approximation and generalized Benders algorithms are provided to solve these problems with nonsmooth convex functions and with conic constraint, respectively. We illustrate these two algorithms by providing detailed procedure of solving several examples. The numerical examples show that outer approximation and generalized Benders decomposition provide a feasible alternative for solving such problems without differentiability.

Suggested Citation

  • Zhou Wei & M. Montaz Ali & Liang Xu & Bo Zeng & Jen-Chih Yao, 2019. "On Solving Nonsmooth Mixed-Integer Nonlinear Programming Problems by Outer Approximation and Generalized Benders Decomposition," Journal of Optimization Theory and Applications, Springer, vol. 181(3), pages 840-863, June.
    • Handle: RePEc:spr:joptap:v:181:y:2019:i:3:d:10.1007_s10957-019-01499-7
    DOI: 10.1007/s10957-019-01499-7
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    References listed on IDEAS

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    1. Omprakash K. Gupta & A. Ravindran, 1985. "Branch and Bound Experiments in Convex Nonlinear Integer Programming," Management Science, INFORMS, vol. 31(12), pages 1533-1546, December.
    2. J. N. Hooker, 2007. "Planning and Scheduling by Logic-Based Benders Decomposition," Operations Research, INFORMS, vol. 55(3), pages 588-602, June.
    3. Zhou Wei & M. Montaz Ali, 2015. "Outer Approximation Algorithm for One Class of Convex Mixed-Integer Nonlinear Programming Problems with Partial Differentiability," Journal of Optimization Theory and Applications, Springer, vol. 167(2), pages 644-652, November.
    4. Boukouvala, Fani & Misener, Ruth & Floudas, Christodoulos A., 2016. "Global optimization advances in Mixed-Integer Nonlinear Programming, MINLP, and Constrained Derivative-Free Optimization, CDFO," European Journal of Operational Research, Elsevier, vol. 252(3), pages 701-727.
    5. Zhou Wei & M. Ali, 2015. "Convex mixed integer nonlinear programming problems and an outer approximation algorithm," Journal of Global Optimization, Springer, vol. 63(2), pages 213-227, October.
    6. Xiang Li & Asgeir Tomasgard & Paul I. Barton, 2011. "Nonconvex Generalized Benders Decomposition for Stochastic Separable Mixed-Integer Nonlinear Programs," Journal of Optimization Theory and Applications, Springer, vol. 151(3), pages 425-454, December.
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    Cited by:

    1. Martina Kuchlbauer & Frauke Liers & Michael Stingl, 2022. "Outer Approximation for Mixed-Integer Nonlinear Robust Optimization," Journal of Optimization Theory and Applications, Springer, vol. 195(3), pages 1056-1086, December.

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