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A multiplicative weights update algorithm for MINLP

Author

Listed:
  • Luca Mencarelli

    (CNRS LIX, École Polytechnique)

  • Youcef Sahraoui

    (CNRS LIX, École Polytechnique
    OSIRIS, EDF R&D)

  • Leo Liberti

    (CNRS LIX, École Polytechnique)

Abstract

We discuss an application of the well-known multiplicative weights update (MWU) algorithm to non-convex and mixed-integer non-linear programming. We present applications to: (a) the distance geometry problem, which arises in the positioning of mobile sensors and in protein conformation; (b) a hydro unit commitment problem arising in the energy industry, and (c) a class of Markowitz’ portfolio selection problems. The interest of the MWU with respect to one of its closest competitors (classic multi-start) is that it provides a relative approximation guarantee on a certain quality measure of the solution.

Suggested Citation

  • Luca Mencarelli & Youcef Sahraoui & Leo Liberti, 2017. "A multiplicative weights update algorithm for MINLP," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 5(1), pages 31-86, March.
    • Handle: RePEc:spr:eurjco:v:5:y:2017:i:1:d:10.1007_s13675-016-0069-8
    DOI: 10.1007/s13675-016-0069-8
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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. Serge A. Plotkin & David B. Shmoys & Éva Tardos, 1995. "Fast Approximation Algorithms for Fractional Packing and Covering Problems," Mathematics of Operations Research, INFORMS, vol. 20(2), pages 257-301, May.
    3. Alberto Borghetti & Claudia D’Ambrosio & Andrea Lodi & Silvano Martello, 2015. "Optimal Scheduling of a Multiunit Hydro Power Station in a Short-Term Planning Horizon," International Series in Operations Research & Management Science, in: Katta G. Murty (ed.), Case Studies in Operations Research, edition 127, chapter 8, pages 167-181, Springer.
    4. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    5. Hansen, Pierre & Mladenovic, Nenad, 2001. "Variable neighborhood search: Principles and applications," European Journal of Operational Research, Elsevier, vol. 130(3), pages 449-467, May.
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    Cited by:

    1. Leo Liberti, 2020. "Distance geometry and data science," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(2), pages 271-339, July.

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