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Conditioning of convex piecewise linear stochastic programs

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 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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Received: May 2000 / Accepted: May 2002-07-16 Published online: September 5, 2002


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).

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