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Efficient solution of quadratically constrained quadratic subproblems within the mesh adaptive direct search algorithm

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  • Amaioua, Nadir
  • Audet, Charles
  • Conn, Andrew R.
  • Le Digabel, Sébastien

Abstract

The mesh adaptive direct search algorithm (MADS) is an iterative method for constrained blackbox optimization problems. One of the optional MADS features is a versatile search step in which quadratic models are built leading to a series of quadratically constrained quadratic subproblems. This work explores different algorithms that exploit the structure of the quadratic models: the first one applies an l1-exact penalty function, the second uses an augmented Lagrangian and the third one combines the former two, resulting in a new algorithm. It is notable that this latter approach is uniquely suitable for quadratically constrained quadratic problems. These methods are implemented within the NOMAD software package and their impact are assessed through computational experiments on 65 analytical test problems and 4 simulation-based engineering applications.

Suggested Citation

  • Amaioua, Nadir & Audet, Charles & Conn, Andrew R. & Le Digabel, Sébastien, 2018. "Efficient solution of quadratically constrained quadratic subproblems within the mesh adaptive direct search algorithm," European Journal of Operational Research, Elsevier, vol. 268(1), pages 13-24.
    • Handle: RePEc:eee:ejores:v:268:y:2018:i:1:p:13-24
    DOI: 10.1016/j.ejor.2017.10.058
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    References listed on IDEAS

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    1. Audet, Charles & Savard, Gilles & Zghal, Walid, 2010. "A mesh adaptive direct search algorithm for multiobjective optimization," European Journal of Operational Research, Elsevier, vol. 204(3), pages 545-556, August.
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    4. Willard I. Zangwill, 1967. "Non-Linear Programming Via Penalty Functions," Management Science, INFORMS, vol. 13(5), pages 344-358, January.
    5. 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.
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    Cited by:

    1. Pooriya Beyhaghi & Ryan Alimo & Thomas Bewley, 2020. "A derivative-free optimization algorithm for the efficient minimization of functions obtained via statistical averaging," Computational Optimization and Applications, Springer, vol. 76(1), pages 1-31, May.
    2. Árpád Bűrmen & Iztok Fajfar, 2019. "Mesh adaptive direct search with simplicial Hessian update," Computational Optimization and Applications, Springer, vol. 74(3), pages 645-667, December.

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