Continuous approximation schemes for stochastic programs

John R. Birge, Liqun Qi

Research output: Journal article publicationJournal articleAcademic researchpeer-review

7 Citations (Scopus)


One of the main methods for solving stochastic programs is approximation by discretizing the probability distribution. However, discretization may lose differentiability of expectational functionals. The complexity of discrete approximation schemes also increases exponentially as the dimension of the random vector increases. On the other hand, stochastic methods can solve stochastic programs with larger dimensions but their convergence is in the sense of probability one. In this paper, we study the differentiability property of stochastic two-stage programs and discuss continuous approximation methods for stochastic programs. We present several ways to calculate and estimate this derivative. We then design several continuous approximation schemes and study their convergence behavior and implementation. The methods include several types of truncation approximation, lower dimensional approximation and limited basis approximation. Baltzer AG, Science Publishers.
Original languageEnglish
Pages (from-to)15-38
Number of pages24
JournalAnnals of Operations Research
Issue number1
Publication statusPublished - 1 Dec 1995
Externally publishedYes


  • Approximation
  • continuous distribution
  • derivative
  • stochastic programming

ASJC Scopus subject areas

  • Management Science and Operations Research
  • General Decision Sciences


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