Conditioning of convex piecewise linear stochastic programs

Alexander Shapiro, Tito Homem-De-Mello, Joocheol Kim

Research output: Contribution to journalArticle

41 Citations (Scopus)

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 languageEnglish
Pages (from-to)1-19
Number of pages19
JournalMathematical Programming, Series B
Volume94
Issue number1
DOIs
Publication statusPublished - 2002 Dec 1

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Conditioning
Piecewise Linear
Stochastic programming
Condition number
Optimal Solution
Ill-conditioning
Stochastic Programming
Random Function
Expected Value
Large Deviations
Linear Function
Sample Size
Objective function
Directly proportional
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All Science Journal Classification (ASJC) codes

  • Software
  • Mathematics(all)

Cite this

Shapiro, Alexander ; Homem-De-Mello, Tito ; Kim, Joocheol. / Conditioning of convex piecewise linear stochastic programs. In: Mathematical Programming, Series B. 2002 ; Vol. 94, No. 1. pp. 1-19.
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Conditioning of convex piecewise linear stochastic programs. / Shapiro, Alexander; Homem-De-Mello, Tito; Kim, Joocheol.

In: Mathematical Programming, Series B, Vol. 94, No. 1, 01.12.2002, p. 1-19.

Research output: Contribution to journalArticle

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