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Stochastic mesh adaptive direct search for blackbox optimization using probabilistic estimates

Author

Listed:
  • Charles Audet

    (Polytechnique Montréal)

  • Kwassi Joseph Dzahini

    (Polytechnique Montréal)

  • Michael Kokkolaras

    (McGill University)

  • Sébastien Le Digabel

    (Polytechnique Montréal)

Abstract

We present a stochastic extension of the mesh adaptive direct search (MADS) algorithm originally developed for deterministic blackbox optimization. The algorithm, called StoMADS, considers the unconstrained optimization of an objective function f whose values can be computed only through a blackbox corrupted by some random noise following an unknown distribution. The proposed method is based on an algorithmic framework similar to that of MADS and uses random estimates of function values obtained from stochastic observations since the exact deterministic computable version of f is not available. Such estimates are required to be accurate with a sufficiently large but fixed probability and to satisfy a variance condition. The ability of the proposed algorithm to generate an asymptotically dense set of search directions is then exploited using martingale theory to prove convergence to a Clarke stationary point of f with probability one.

Suggested Citation

  • Charles Audet & Kwassi Joseph Dzahini & Michael Kokkolaras & Sébastien Le Digabel, 2021. "Stochastic mesh adaptive direct search for blackbox optimization using probabilistic estimates," Computational Optimization and Applications, Springer, vol. 79(1), pages 1-34, May.
    • Handle: RePEc:spr:coopap:v:79:y:2021:i:1:d:10.1007_s10589-020-00249-0
    DOI: 10.1007/s10589-020-00249-0
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    References listed on IDEAS

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    1. Angun, M.E. & Kleijnen, Jack P.C., 2012. "An asymptotic test of optimality conditions in multiresponse simulation optimization," Other publications TiSEM a69dfa59-b0e1-45bd-8cd6-a, Tilburg University, School of Economics and Management.
    2. Nicholas Gould & Dominique Orban & Philippe Toint, 2015. "CUTEst: a Constrained and Unconstrained Testing Environment with safe threads for mathematical optimization," Computational Optimization and Applications, Springer, vol. 60(3), pages 545-557, April.
    3. Ebru Angün & Jack Kleijnen, 2012. "An Asymptotic Test of Optimality Conditions in Multiresponse Simulation Optimization," INFORMS Journal on Computing, INFORMS, vol. 24(1), pages 53-65, February.
    4. Chang, Kuo-Hao, 2012. "Stochastic Nelder–Mead simplex method – A new globally convergent direct search method for simulation optimization," European Journal of Operational Research, Elsevier, vol. 220(3), pages 684-694.
    5. Jeffrey Larson & Stephen C. Billups, 2016. "Stochastic derivative-free optimization using a trust region framework," Computational Optimization and Applications, Springer, vol. 64(3), pages 619-645, July.
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    Cited by:

    1. Andrea Brilli & Morteza Kimiaei & Giampaolo Liuzzi & Stefano Lucidi, 2024. "Worst Case Complexity Bounds for Linesearch-Type Derivative-Free Algorithms," Journal of Optimization Theory and Applications, Springer, vol. 203(1), pages 419-454, October.
    2. Kwassi Joseph Dzahini, 2022. "Expected complexity analysis of stochastic direct-search," Computational Optimization and Applications, Springer, vol. 81(1), pages 179-200, January.
    3. Youssef Diouane & Victor Picheny & Rodolophe Le Riche & Alexandre Scotto Di Perrotolo, 2023. "TREGO: a trust-region framework for efficient global optimization," Journal of Global Optimization, Springer, vol. 86(1), pages 1-23, May.

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