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Alternative regularizations for Outer-Approximation algorithms for convex MINLP

Author

Listed:
  • David E. Bernal

    (NASA Ames Research Center
    Universities Space Research Association
    Carnegie Mellon University)

  • Zedong Peng

    (Zhejiang University
    Business Growth BU, JD.com)

  • Jan Kronqvist

    (KTH Royal Institute of Technology
    Imperial College London)

  • Ignacio E. Grossmann

    (Carnegie Mellon University)

Abstract

In this work, we extend the regularization framework from Kronqvist et al. (Math Program 180(1):285–310, 2020) by incorporating several new regularization functions and develop a regularized single-tree search method for solving convex mixed-integer nonlinear programming (MINLP) problems. We propose a set of regularization functions based on distance metrics and Lagrangean approximations, used in the projection problem for finding new integer combinations to be used within the Outer-Approximation (OA) method. The new approach, called Regularized Outer-Approximation (ROA), has been implemented as part of the open-source Mixed-integer nonlinear decomposition toolbox for Pyomo—MindtPy. We compare the OA method with seven regularization function alternatives for ROA. Moreover, we extend the LP/NLP Branch and Bound method proposed by Quesada and Grossmann (Comput Chem Eng 16(10–11):937–947, 1992) to include regularization in an algorithm denoted RLP/NLP. We provide convergence guarantees for both ROA and RLP/NLP. Finally, we perform an extensive computational experiment considering all convex MINLP problems in the benchmark library MINLPLib. The computational results show clear advantages of using regularization combined with the OA method.

Suggested Citation

  • David E. Bernal & Zedong Peng & Jan Kronqvist & Ignacio E. Grossmann, 2022. "Alternative regularizations for Outer-Approximation algorithms for convex MINLP," Journal of Global Optimization, Springer, vol. 84(4), pages 807-842, December.
    • Handle: RePEc:spr:jglopt:v:84:y:2022:i:4:d:10.1007_s10898-022-01178-4
    DOI: 10.1007/s10898-022-01178-4
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    References listed on IDEAS

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    7. 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.
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    Cited by:

    1. N. Krejić & E. H. M. Krulikovski & M. Raydan, 2023. "A Low-Cost Alternating Projection Approach for a Continuous Formulation of Convex and Cardinality Constrained Optimization," SN Operations Research Forum, Springer, vol. 4(4), pages 1-24, December.

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