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A derivative-free algorithm for linearly constrained optimization problems

Author

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  • E. Gumma
  • M. Hashim
  • M. Ali

Abstract

Based on the NEWUOA algorithm, a new derivative-free algorithm is developed, named LCOBYQA. The main aim of the algorithm is to find a minimizer $x^{*} \in\mathbb{R}^{n}$ of a non-linear function, whose derivatives are unavailable, subject to linear inequality constraints. The algorithm is based on the model of the given function constructed from a set of interpolation points. LCOBYQA is iterative, at each iteration it constructs a quadratic approximation (model) of the objective function that satisfies interpolation conditions, and leaves some freedom in the model. The remaining freedom is resolved by minimizing the Frobenius norm of the change to the second derivative matrix of the model. The model is then minimized by a trust-region subproblem using the conjugate gradient method for a new iterate. At times the new iterate is found from a model iteration, designed to improve the geometry of the interpolation points. Numerical results are presented which show that LCOBYQA works well and is very competing against available model-based derivative-free algorithms. Copyright Springer Science+Business Media New York 2014

Suggested Citation

  • 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.
    • Handle: RePEc:spr:coopap:v:57:y:2014:i:3:p:599-621
    DOI: 10.1007/s10589-013-9607-y
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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. Adriano Verdério & Elizabeth W. Karas & Lucas G. Pedroso & Katya Scheinberg, 2017. "On the construction of quadratic models for derivative-free trust-region algorithms," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 5(4), pages 501-527, December.
    3. Charles Audet & Andrew R. Conn & Sébastien Le Digabel & Mathilde Peyrega, 2018. "A progressive barrier derivative-free trust-region algorithm for constrained optimization," Computational Optimization and Applications, Springer, vol. 71(2), pages 307-329, November.

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