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Why Does Monte Carlo Fail to Work Properly in High-Dimensional Optimization Problems?

Author

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  • Boris Polyak

    (Institute for Control Sciences, RAS)

  • Pavel Shcherbakov

    (Institute for Control Sciences, RAS)

Abstract

The paper presents a quantitative explanation of failure of generic Monte Carlo techniques as applied to optimization problems of high dimensions. Deterministic grids are also discussed.

Suggested Citation

  • Boris Polyak & Pavel Shcherbakov, 2017. "Why Does Monte Carlo Fail to Work Properly in High-Dimensional Optimization Problems?," Journal of Optimization Theory and Applications, Springer, vol. 173(2), pages 612-627, May.
    • Handle: RePEc:spr:joptap:v:173:y:2017:i:2:d:10.1007_s10957-016-1045-4
    DOI: 10.1007/s10957-016-1045-4
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    References listed on IDEAS

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    1. Roman Statnikov & Josef Matusov & Alexander Statnikov, 2012. "Multicriteria Engineering Optimization Problems: Statement, Solution and Applications," Journal of Optimization Theory and Applications, Springer, vol. 155(2), pages 355-375, November.
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    Cited by:

    1. Pavel Shcherbakov & Mingyue Ding & Ming Yuchi, 2021. "Random Sampling Many-Dimensional Sets Arising in Control," Mathematics, MDPI, vol. 9(5), pages 1-16, March.
    2. E. A. Tsvetkov & R. A. Krymov, 2022. "Pure Random Search with Virtual Extension of Feasible Region," Journal of Optimization Theory and Applications, Springer, vol. 195(2), pages 575-595, November.

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