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Stopping Rules for Optimization Algorithms Based on Stochastic Approximation

Author

Listed:
  • Takayuki Wada

    (Osaka University)

  • Yasumasa Fujisaki

    (Osaka University)

Abstract

Stopping rules are developed for stochastic optimization algorithms, which minimize an unknown objective function using noise corrupted measurements. In particular, the finite-difference stochastic approximation and the simultaneous perturbation stochastic approximation are considered. The candidate solution after an adequate number of iterations is shown to be sufficiently close to the optimal solution in a mean squared sense. These numbers are determined by a priori information only. Furthermore, it is shown that these are polynomial order of the problem size.

Suggested Citation

  • Takayuki Wada & Yasumasa Fujisaki, 2016. "Stopping Rules for Optimization Algorithms Based on Stochastic Approximation," Journal of Optimization Theory and Applications, Springer, vol. 169(2), pages 568-586, May.
    • Handle: RePEc:spr:joptap:v:169:y:2016:i:2:d:10.1007_s10957-015-0808-7
    DOI: 10.1007/s10957-015-0808-7
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    References listed on IDEAS

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    1. Mark Broadie & Deniz Cicek & Assaf Zeevi, 2011. "General Bounds and Finite-Time Improvement for the Kiefer-Wolfowitz Stochastic Approximation Algorithm," Operations Research, INFORMS, vol. 59(5), pages 1211-1224, October.
    2. G. Yin & J. W. Wang & Q. Zhang & Y. J. Liu, 2006. "Stochastic Optimization Algorithms for Pricing American Put Options Under Regime-Switching Models," Journal of Optimization Theory and Applications, Springer, vol. 131(1), pages 37-52, October.
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    Cited by:

    1. Miloje S. Radenković & Miloš S. Stanković & Srdjan S. Stanković, 2018. "On Stochastic Extremum Seeking via Adaptive Perturbation–Demodulation Loop," Journal of Optimization Theory and Applications, Springer, vol. 179(3), pages 1008-1024, December.

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