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A trust-region-based derivative free algorithm for mixed integer programming

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  • Eric Newby
  • M. Ali

Abstract

A trust-region-based derivative free algorithm for solving bound constrained mixed integer nonlinear programs is developed in this paper. The algorithm is proven to converge to a local minimum after a finite number of function evaluations. In addition, an improved definition of local minima of mixed integer programs is proposed. Computational results showing the effectiveness of the derivative free algorithm are presented. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • 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.
    • Handle: RePEc:spr:coopap:v:60:y:2015:i:1:p:199-229
    DOI: 10.1007/s10589-014-9660-1
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. A. Custódio & H. Rocha & L. Vicente, 2010. "Incorporating minimum Frobenius norm models in direct search," Computational Optimization and Applications, Springer, vol. 46(2), pages 265-278, June.
    4. Duan Li & Xiaoling Sun, 2006. "Nonlinear Integer Programming," International Series in Operations Research and Management Science, Springer, number 978-0-387-32995-6, December.
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    Cited by:

    1. Ubaldo M. García Palomares, 2023. "Convergence of derivative-free nonmonotone Direct Search Methods for unconstrained and box-constrained mixed-integer optimization," Computational Optimization and Applications, Springer, vol. 85(3), pages 821-856, July.
    2. 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.
    3. 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.
    4. Burcu Beykal & Styliani Avraamidou & Ioannis P. E. Pistikopoulos & Melis Onel & Efstratios N. Pistikopoulos, 2020. "DOMINO: Data-driven Optimization of bi-level Mixed-Integer NOnlinear Problems," Journal of Global Optimization, Springer, vol. 78(1), pages 1-36, September.

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