Conditioning of convex piecewise linear stochastic programs

Conditioning of convex piecewise linear stochastic programs

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Article ID: iaor20032541
Country: Germany
Volume: 94
Issue: 1
Start Page Number: 1
End Page Number: 19
Publication Date: Jan 2002
Journal: Mathematical Programming
Authors: , ,
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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