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A Distributed Interior-Point KKT Solver for Multistage Stochastic Optimization

Author

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  • Jens Hübner

    (HaCon Ingenieurgesellschaft mbH, 30163 Hannover, Germany)

  • Martin Schmidt

    (Department Mathematik, Friedrich-Alexander-Universität Erlangen-Nürnberg, 91058 Erlangen, Germany; and Energie Campus Nürnberg, 90429 Nürnberg, Germany)

  • Marc C. Steinbach

    (Leibniz Universität Hannover, Institute of Applied Mathematics, 30167 Hannover, Germany)

Abstract

Multistage stochastic optimization leads to NLPs over scenario trees that become extremely large when many time stages or fine discretizations of the probability space are required. Interior-point methods are well suited for these problems if the arising huge, structured KKT systems can be solved efficiently, for instance, with a large scenario tree but a moderate number of variables per node. For this setting we develop a distributed implementation based on data parallelism in a depth-first distribution of the scenario tree over the processes. Our theoretical analysis predicts very low memory and communication overheads. Detailed computational experiments confirm this prediction and demonstrate the overall performance of the algorithm. We solve multistage stochastic quadratic programs with up to 400 × 10 6 variables and 8.59 × 10 9 KKT matrix entries or 136 × 10 6 variables and 12.6 × 10 9 entries on a compute cluster with 384 GB RAM.

Suggested Citation

  • Jens Hübner & Martin Schmidt & Marc C. Steinbach, 2017. "A Distributed Interior-Point KKT Solver for Multistage Stochastic Optimization," INFORMS Journal on Computing, INFORMS, vol. 29(4), pages 612-630, November.
    • Handle: RePEc:inm:orijoc:v:29:y:2017:i:4:p:612-630
    DOI: 10.1287/ijoc.2017.0748
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    References listed on IDEAS

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    1. Blomvall, Jorgen & Lindberg, Per Olov, 2002. "A Riccati-based primal interior point solver for multistage stochastic programming," European Journal of Operational Research, Elsevier, vol. 143(2), pages 452-461, December.
    2. Jacek Gondzio & Andreas Grothey, 2009. "Exploiting structure in parallel implementation of interior point methods for optimization," Computational Management Science, Springer, vol. 6(2), pages 135-160, May.
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    Cited by:

    1. Castro, Jordi & Escudero, Laureano F. & Monge, Juan F., 2023. "On solving large-scale multistage stochastic optimization problems with a new specialized interior-point approach," European Journal of Operational Research, Elsevier, vol. 310(1), pages 268-285.
    2. Jens Hübner & Martin Schmidt & Marc C. Steinbach, 2020. "Optimization techniques for tree-structured nonlinear problems," Computational Management Science, Springer, vol. 17(3), pages 409-436, October.
    3. Schryen, Guido, 2020. "Parallel computational optimization in operations research: A new integrative framework, literature review and research directions," European Journal of Operational Research, Elsevier, vol. 287(1), pages 1-18.

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