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Mesh adaptive direct search with simplicial Hessian update

Author

Listed:
  • Árpád Bűrmen

    (University of Ljubljana)

  • Iztok Fajfar

    (University of Ljubljana)

Abstract

Recently a second directional derivative-based Hessian updating formula was used for Hessian approximation in mesh adaptive direct search (MADS). The approach combined with a quadratic program solver significantly improves the performance of MADS. Unfortunately it imposes some strict requirements on the position of points and the order in which they are evaluated. The subject of this paper is the introduction of a Hessian update formula that utilizes the points from the neighborhood of the incumbent solution without imposing such strict restrictions. The obtained approximate Hessian can then be used for constructing a quadratic model of the objective and the constraints. The proposed algorithm was compared to the reference implementation of MADS (NOMAD) on four sets of test problems. On all but one of them it outperformed NOMAD. The biggest performance difference was observed on constrained problems. To validate the algorithm further the approach was tested on several real-world optimization problems arising from yield approximation and worst case analysis in integrated circuit design. On all tested problems the proposed approach outperformed NOMAD.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:coopap:v:74:y:2019:i:3:d:10.1007_s10589-019-00133-6
    DOI: 10.1007/s10589-019-00133-6
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    References listed on IDEAS

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    1. Benjamin Dyke & Thomas J. Asaki, 2013. "Using QR Decomposition to Obtain a New Instance of Mesh Adaptive Direct Search with Uniformly Distributed Polling Directions," Journal of Optimization Theory and Applications, Springer, vol. 159(3), pages 805-821, December.
    2. 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.
    3. Árpád Bűrmen & Jernej Olenšek & Tadej Tuma, 2015. "Mesh adaptive direct search with second directional derivative-based Hessian update," Computational Optimization and Applications, Springer, vol. 62(3), pages 693-715, December.
    4. I. D. Coope & C. J. Price, 2000. "Frame Based Methods for Unconstrained Optimization," Journal of Optimization Theory and Applications, Springer, vol. 107(2), pages 261-274, November.
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    Cited by:

    1. Árpád Bűrmen & Tadej Tuma & Jernej Olenšek, 2021. "Randomized Simplicial Hessian Update," Mathematics, MDPI, vol. 9(15), pages 1-18, July.

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