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Nonconvex Generalized Benders Decomposition for Stochastic Separable Mixed-Integer Nonlinear Programs

Author

Listed:
  • Xiang Li

    (Massachusetts Institute of Technology)

  • Asgeir Tomasgard

    (Norwegian University of Science and Technology)

  • Paul I. Barton

    (Massachusetts Institute of Technology)

Abstract

This paper considers deterministic global optimization of scenario-based, two-stage stochastic mixed-integer nonlinear programs (MINLPs) in which the participating functions are nonconvex and separable in integer and continuous variables. A novel decomposition method based on generalized Benders decomposition, named nonconvex generalized Benders decomposition (NGBD), is developed to obtain ε-optimal solutions of the stochastic MINLPs of interest in finite time. The dramatic computational advantage of NGBD over state-of-the-art global optimizers is demonstrated through the computational study of several engineering problems, where a problem with almost 150,000 variables is solved by NGBD within 80 minutes of solver time.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:151:y:2011:i:3:d:10.1007_s10957-011-9888-1
    DOI: 10.1007/s10957-011-9888-1
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    References listed on IDEAS

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