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Conditioning of convex piecewise linear stochastic programs

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Abstract.

 In this paper we consider stochastic programming problems where the objective function is given as an expected value of a convex piecewise linear random function. With an optimal solution of such a problem we associate a condition number which characterizes well or ill conditioning of the problem. Using theory of Large Deviations we show that the sample size needed to calculate the optimal solution of such problem with a given probability is approximately proportional to the condition number.

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Authors and Affiliations

  1. School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332-0205, USA, e-mail: ashapiro@isye.gatech.edu, , , , , , US

    Alexander Shapiro

  2. Department of Industrial, Welding and Systems Engineering, The Ohio State University, 1971 Neil Ave., Columbus, Ohio 43210-1271, USA, e-mail: homem-de-mello.1@osu.edu, , , , , , US

    Tito Homem-de-Mello

  3. School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332-0205, USA, , , , , , US

    Joocheol Kim

Authors
  1. Alexander Shapiro
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  2. Tito Homem-de-Mello
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  3. Joocheol Kim
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Received: May 2000 / Accepted: May 2002-07-16 Published online: September 5, 2002

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The research of this author was supported, in part, by grant DMS-0073770 from the National Science Foundation

Key Words. stochastic programming – Monte Carlo simulation – large deviations theory – ill-conditioned problems

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Shapiro, A., Homem-de-Mello, T. & Kim, J. Conditioning of convex piecewise linear stochastic programs. Math. Program., Ser. A 94, 1–19 (2002). https://doi.org/10.1007/s10107-002-0313-2

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  • DOI: https://doi.org/10.1007/s10107-002-0313-2

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