### 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 1 |

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### All Science Journal Classification (ASJC) codes

- Software
- Mathematics(all)

### Cite this

*Mathematical Programming, Series B*,

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

}

*Mathematical Programming, Series B*, vol. 94, no. 1, pp. 1-19. https://doi.org/10.1007/s10107-002-0313-2

**Conditioning of convex piecewise linear stochastic programs.** / Shapiro, Alexander; Homem-De-Mello, Tito; Kim, Joocheol.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Conditioning of convex piecewise linear stochastic programs

AU - Shapiro, Alexander

AU - Homem-De-Mello, Tito

AU - Kim, Joocheol

PY - 2002/12/1

Y1 - 2002/12/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=3943087919&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=3943087919&partnerID=8YFLogxK

U2 - 10.1007/s10107-002-0313-2

DO - 10.1007/s10107-002-0313-2

M3 - Article

AN - SCOPUS:3943087919

VL - 94

SP - 1

EP - 19

JO - Mathematical Programming

JF - Mathematical Programming

SN - 0025-5610

IS - 1

ER -