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Derivative-free methods for bound constrained mixed-integer optimization

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  • G. Liuzzi
  • S. Lucidi
  • F. Rinaldi

Abstract

We consider the problem of minimizing a continuously differentiable function of several variables subject to simple bound constraints where some of the variables are restricted to take integer values. We assume that the first order derivatives of the objective function can be neither calculated nor approximated explicitly. This class of mixed integer nonlinear optimization problems arises frequently in many industrial and scientific applications and this motivates the increasing interest in the study of derivative-free methods for their solution. The continuous variables are handled by a linesearch strategy whereas to tackle the discrete ones we employ a local search-type approach. We propose different algorithms which are characterized by the way the current iterate is updated and by the stationarity conditions satisfied by the limit points of the sequences they produce. Copyright Springer Science+Business Media, LLC 2012

Suggested Citation

  • G. Liuzzi & S. Lucidi & F. Rinaldi, 2012. "Derivative-free methods for bound constrained mixed-integer optimization," Computational Optimization and Applications, Springer, vol. 53(2), pages 505-526, October.
    • Handle: RePEc:spr:coopap:v:53:y:2012:i:2:p:505-526
    DOI: 10.1007/s10589-011-9405-3
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    References listed on IDEAS

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    1. C. J. Lin & S. Lucidi & L. Palagi & A. Risi & M. Sciandrone, 2009. "Decomposition Algorithm Model for Singly Linearly-Constrained Problems Subject to Lower and Upper Bounds," Journal of Optimization Theory and Applications, Springer, vol. 141(1), pages 107-126, April.
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    Cited by:

    1. Angelo Ciccazzo & Gianni Di Pillo & Vittorio Latorre, 2015. "A SVM Surrogate Model Based Method for Yield Optimization in Electronic Circuit Design," DIAG Technical Reports 2015-03, Department of Computer, Control and Management Engineering, Universita' degli Studi di Roma "La Sapienza".
    2. Tommaso Giovannelli & Giampaolo Liuzzi & Stefano Lucidi & Francesco Rinaldi, 2022. "Derivative-free methods for mixed-integer nonsmooth constrained optimization," Computational Optimization and Applications, Springer, vol. 82(2), pages 293-327, June.
    3. Stefano Lucidi & Massimo Maurici & Luca Paulon & Francesco Rinaldi & Massimo Roma, 2014. "A derivative-free approach for a simulation-based optimization problem in healthcare," DIAG Technical Reports 2014-15, Department of Computer, Control and Management Engineering, Universita' degli Studi di Roma "La Sapienza".
    4. L. Grippo & F. Rinaldi, 2015. "A class of derivative-free nonmonotone optimization algorithms employing coordinate rotations and gradient approximations," Computational Optimization and Applications, Springer, vol. 60(1), pages 1-33, January.
    5. Nikolaos Ploskas & Nikolaos V. Sahinidis, 2022. "Review and comparison of algorithms and software for mixed-integer derivative-free optimization," Journal of Global Optimization, Springer, vol. 82(3), pages 433-462, March.
    6. 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.
    7. Giampaolo Liuzzi & Stefano Lucidi & Francesco Rinaldi, 2015. "Derivative-Free Methods for Mixed-Integer Constrained Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 164(3), pages 933-965, March.
    8. Eric Newby & M. Ali, 2015. "A trust-region-based derivative free algorithm for mixed integer programming," Computational Optimization and Applications, Springer, vol. 60(1), pages 199-229, January.
    9. Angelo Ciccazzo & Vittorio Latorre & Giampaolo Liuzzi & Stefano Lucidi & Francesco Rinaldi, 2015. "Derivative-Free Robust Optimization for Circuit Design," Journal of Optimization Theory and Applications, Springer, vol. 164(3), pages 842-861, March.

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