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A Primal-Dual Decomposition Algorithm for Multistage Stochastic Convex Programming

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Abstract

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.

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Authors and Affiliations

  1. World Bank Treasury, World Bank, United States of America

    Arjan Berkelaar

  2. Vrije Universiteit, The Netherlands & ORTEC International, Amsterdam, Gouda, The Netherlands

    Joaquim A. S. Gromicho

  3. School of Management, Asian Institute of Technology, Thailand

    Roy Kouwenberg

  4. Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, Shatin, Hong Kong

    Shuzhong Zhang

Authors
  1. Arjan Berkelaar
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  2. Joaquim A. S. Gromicho
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  3. Roy Kouwenberg
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  4. Shuzhong Zhang
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Corresponding author

Correspondence to Shuzhong Zhang.

Additional information

Research supported by Hong Kong RGC Earmarked Grant CUHK4233/01E.

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Berkelaar, A., Gromicho, J., Kouwenberg, R. et al. A Primal-Dual Decomposition Algorithm for Multistage Stochastic Convex Programming. Math. Program. 104, 153–177 (2005). https://doi.org/10.1007/s10107-005-0575-6

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  • DOI: https://doi.org/10.1007/s10107-005-0575-6

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