A primal-dual decomposition algorithm for multistage stochastic convex programming

Arjan Berkelaar, Joaquim A S Gromicho, Roy Kouwenberg, Shuzhong Zhang

Research output: Contribution to journalArticlepeer-review

16 Scopus citations


This paper presents a new and high performance solution method for multistage stochastic convex programming. Stochastic programming is a quantitative tool developed in the field of optimization to cope with the problem of decision-making under uncertainty. Among others, stochastic programming has found many applications in finance, such as asset-liability and bond-portfolio management. However, many stochastic programming applications still remain computationally intractable because of their overwhelming dimensionality. In this paper we propose a new decomposition algorithm for multistage stochastic programming with a convex objective and stochastic recourse matrices, based on the path-following interior point method combined with the homogeneous self-dual embedding technique. Our preliminary numerical experiments show that this approach is very promising in many ways for solving generic multistage stochastic programming, including its superiority in terms of numerical efficiency, as well as the flexibility in testing and analyzing the model.

Original languageEnglish (US)
Pages (from-to)153-177
Number of pages25
JournalMathematical Programming
Issue number1
StatePublished - Sep 1 2005


  • Convex objective
  • Homogeneous self-dual embedding
  • Interior point method
  • Multistage stochastic programming


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