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A new hybrid stochastic approximation algorithm

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Abstract

In this paper, we consider optimizing the performance of a stochastic system that is too complex for theoretical analysis to be possible, but can be evaluated by using simulation or direct experimentation. To optimize the expected performance of such system as a function of several input parameters, we propose a hybrid stochastic approximation algorithm for finding the root of the gradient of the response function. At each iteration of the hybrid algorithm, alternatively, either an average of two independent noisy negative gradient directions or a scaled noisy negative gradient direction is selected. The almost sure convergence of the hybrid algorithm is established. Numerical comparisons of the hybrid algorithm with two other existing algorithms in a simple queueing system and five nonlinear unconstrained stochastic optimization problems show the advantage of the hybrid algorithm.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Shanghai University, Shanghai, 200444, People’s Republic of China

    Zi Xu

  2. School of Mathematical Sciences, Fudan University, Shanghai, 200433, People’s Republic of China

    Xinming Wu

Authors
  1. Zi Xu
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  2. Xinming Wu
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Corresponding author

Correspondence to Xinming Wu.

Additional information

Z. Xu was supported by China NSF under the Grant 11101261 and Key Disciplines of Shanghai Municipality (S30104).

X. Wu was supported by China NSF under the Grant 11026036.

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Xu, Z., Wu, X. A new hybrid stochastic approximation algorithm. Optim Lett 7, 593–606 (2013). https://doi.org/10.1007/s11590-012-0443-2

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  • DOI: https://doi.org/10.1007/s11590-012-0443-2

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