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Derivative-free methods for mixed-integer nonsmooth constrained optimization

Author

Listed:
  • Tommaso Giovannelli

    (Lehigh University)

  • Giampaolo Liuzzi

    (Sapienza Università di Roma and Istituto di Analisi dei Sistemi e Informatica (IASI), CNR)

  • Stefano Lucidi

    (Sapienza Università di Roma)

  • Francesco Rinaldi

    (Università di Padova)

Abstract

In this paper, mixed-integer nonsmooth constrained optimization problems are considered, where objective/constraint functions are available only as the output of a black-box zeroth-order oracle that does not provide derivative information. A new derivative-free linesearch-based algorithmic framework is proposed to suitably handle those problems. First, a scheme for bound constrained problems that combines a dense sequence of directions to handle the nonsmoothness of the objective function with primitive directions to handle discrete variables is described. Then, an exact penalty approach is embedded in the scheme to suitably manage nonlinear (possibly nonsmooth) constraints. Global convergence properties of the proposed algorithms toward stationary points are analyzed and results of an extensive numerical experience on a set of mixed-integer test problems are reported.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:coopap:v:82:y:2022:i:2:d:10.1007_s10589-022-00363-1
    DOI: 10.1007/s10589-022-00363-1
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    References listed on IDEAS

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    1. Jeffrey Larson & Sven Leyffer & Prashant Palkar & Stefan M. Wild, 2021. "A method for convex black-box integer global optimization," Journal of Global Optimization, Springer, vol. 80(2), pages 439-477, June.
    2. 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.
    3. Sriver, Todd A. & Chrissis, James W. & Abramson, Mark A., 2009. "Pattern search ranking and selection algorithms for mixed variable simulation-based optimization," European Journal of Operational Research, Elsevier, vol. 198(3), pages 878-890, November.
    4. Charles Audet & J. Dennis & Sébastien Digabel, 2010. "Globalization strategies for Mesh Adaptive Direct Search," Computational Optimization and Applications, Springer, vol. 46(2), pages 193-215, June.
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