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Continuous approximation schemes for stochastic programs

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Abstract

One of the main methods for solving stochastic programs is approximation by discretizing the probability distribution. However, discretization may lose differentiability of expectational functionals. The complexity of discrete approximation schemes also increases exponentially as the dimension of the random vector increases. On the other hand, stochastic methods can solve stochastic programs with larger dimensions but their convergence is in the sense of probability one. In this paper, we study the differentiability property of stochastic two-stage programs and discuss continuous approximation methods for stochastic programs. We present several ways to calculate and estimate this derivative. We then design several continuous approximation schemes and study their convergence behavior and implementation. The methods include several types of truncation approximation, lower dimensional approximation and limited basis approximation.

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Author information

Authors and Affiliations

  1. Department of Industrial and Operations Engineering, University of Michigan, 48109, Ann Arbor, MI, USA

    John R. Birge

  2. School of Mathematics, The University of New South Wales, 2033, Kensington, N.S.W., Australia

    Liqun Qi

Authors
  1. John R. Birge
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  2. Liqun Qi
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Additional information

His work is supported by Office of Naval Research Grant N0014-86-K-0628 and the National Science Foundation under Grant ECS-8815101 and DDM-9215921.

His work is supported by the Australian Research Council.

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Birge, J.R., Qi, L. Continuous approximation schemes for stochastic programs. Ann Oper Res 56, 15–38 (1995). https://doi.org/10.1007/BF02031698

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