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Convergence of derivative-free nonmonotone Direct Search Methods for unconstrained and box-constrained mixed-integer optimization

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  • Ubaldo M. García Palomares

    (Universidade de Vigo)

Abstract

This paper presents a class of nonmonotone Direct Search Methods that converge to stationary points of unconstrained and boxed constrained mixed-integer optimization problems. A new concept is introduced: the quasi-descent direction. A point x is stationary on a set of search directions if there exists no feasible qdd on that set. The method does not require the computation of derivatives nor the explicit manipulation of asymptotically dense matrices. Preliminary numerical experiments carried out on small to medium problems are encouraging.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:coopap:v:85:y:2023:i:3:d:10.1007_s10589-023-00469-0
    DOI: 10.1007/s10589-023-00469-0
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    References listed on IDEAS

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    2. E. Gumma & M. Hashim & M. Ali, 2014. "A derivative-free algorithm for linearly constrained optimization problems," Computational Optimization and Applications, Springer, vol. 57(3), pages 599-621, April.
    3. 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.
    4. 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.
    5. S. Gratton & C. W. Royer & L. N. Vicente & Z. Zhang, 2019. "Direct search based on probabilistic feasible descent for bound and linearly constrained problems," Computational Optimization and Applications, Springer, vol. 72(3), pages 525-559, April.
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