### 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.

Original language | English |
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Pages (from-to) | 1-19 |

Number of pages | 19 |

Journal | Mathematical Programming, Series B |

Volume | 94 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2002 Dec |

### All Science Journal Classification (ASJC) codes

- Software
- Mathematics(all)

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## Cite this

Shapiro, A., Homem-De-Mello, T., & Kim, J. (2002). Conditioning of convex piecewise linear stochastic programs.

*Mathematical Programming, Series B*,*94*(1), 1-19. https://doi.org/10.1007/s10107-002-0313-2