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

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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.

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Authors and Affiliations

  1. Process Systems Engineering Laboratory, Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA

    Xiang Li & Paul I. Barton

  2. Department of Industrial Economics and Technology Management, Norwegian University of Science and Technology, Trondheim, Norway

    Asgeir Tomasgard

Authors
  1. Xiang Li
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  2. Asgeir Tomasgard
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  3. Paul I. Barton
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Correspondence to Paul I. Barton.

Additional information

Communicated by Panos M. Pardalos.

This work was supported by Statoil and the research council of Norway (project nr 176089/S60) as part of the paired Ph.D. research program in gas technologies between MIT and NTNU.

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Li, X., Tomasgard, A. & Barton, P.I. Nonconvex Generalized Benders Decomposition for Stochastic Separable Mixed-Integer Nonlinear Programs. J Optim Theory Appl 151, 425–454 (2011). https://doi.org/10.1007/s10957-011-9888-1

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