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Hierarchical Sparsity in Multistage Stochastic Programs

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Book cover Stochastic Optimization: Algorithms and Applications

Part of the book series: Applied Optimization ((APOP,volume 54))

Abstract

Interior point methods for multistage stochastic programs involve KKT systems with a characteristic global block structure induced by dynamic equations on the scenario tree. We generalize the recursive solution algorithm proposed in an earlier paper so that its linear complexity extends to a refined tree-sparse KKT structure. Then we analyze how the block operations can be specialized to take advantage of problem-specific sparse substructures. Savings of memory and operations for a financial engineering application are discussed in detail.

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Author information

Authors and Affiliations

  1. Konrad-Zuse-Zentrum für Informationstechnik Berlin (ZIB), Takustr. 7, 14195, Berlin, Germany

    Marc C. Steinbach

Authors
  1. Marc C. Steinbach
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Editor information

Editors and Affiliations

  1. Center for Applied Optimization, Department of Industrial and Systems Engineering, University of Florida, USA

    Stanislav Uryasev  & Panos M. Pardalos  & 

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© 2001 Springer Science+Business Media Dordrecht

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Steinbach, M.C. (2001). Hierarchical Sparsity in Multistage Stochastic Programs. In: Uryasev, S., Pardalos, P.M. (eds) Stochastic Optimization: Algorithms and Applications. Applied Optimization, vol 54. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-6594-6_16

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  • DOI: https://doi.org/10.1007/978-1-4757-6594-6_16

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4419-4855-7

  • Online ISBN: 978-1-4757-6594-6

  • eBook Packages: Springer Book Archive

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