IDEAS home Printed from https://ideas.repec.org/a/inm/orijoc/v29y2017i4p612-630.html
   My bibliography  Save this article

A Distributed Interior-Point KKT Solver for Multistage Stochastic Optimization

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://doi.org/10.1287/ijoc.2017.0748
    Download Restriction: no
    File URL: https://libkey.io/10.1287/ijoc.2017.0748?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Gondzio, Jacek & Grothey, Andreas, 2007. "Solving non-linear portfolio optimization problems with the primal-dual interior point method," European Journal of Operational Research, Elsevier, vol. 181(3), pages 1019-1029, September.
    3. 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.
    4. Blomvall, Jörgen & Hagenbjörk, Johan, 2022. "Reducing transaction costs for interest rate risk hedging with stochastic programming," European Journal of Operational Research, Elsevier, vol. 302(3), pages 1282-1293.
    5. Teemu Pennanen & Markku Kallio, 2006. "A splitting method for stochastic programs," Annals of Operations Research, Springer, vol. 142(1), pages 259-268, February.
    6. 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.
    7. Marco Colombo & Andreas Grothey, 2013. "A decomposition-based crash-start for stochastic programming," Computational Optimization and Applications, Springer, vol. 55(2), pages 311-340, June.
    8. Cosmin Petra & Mihai Anitescu, 2012. "A preconditioning technique for Schur complement systems arising in stochastic optimization," Computational Optimization and Applications, Springer, vol. 52(2), pages 315-344, June.
    9. Miles Lubin & J. Hall & Cosmin Petra & Mihai Anitescu, 2013. "Parallel distributed-memory simplex for large-scale stochastic LP problems," Computational Optimization and Applications, Springer, vol. 55(3), pages 571-596, July.
    10. Unai Aldasoro & Laureano Escudero & María Merino & Juan Monge & Gloria Pérez, 2015. "On parallelization of a stochastic dynamic programming algorithm for solving large-scale mixed 0–1 problems under uncertainty," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(3), pages 703-742, October.
    11. Cecilia Orellana Castro & Manolo Rodriguez Heredia & Aurelio R. L. Oliveira, 2023. "Recycling basic columns of the splitting preconditioner in interior point methods," Computational Optimization and Applications, Springer, vol. 86(1), pages 49-78, September.
    12. Ankur Kulkarni & Uday Shanbhag, 2012. "Recourse-based stochastic nonlinear programming: properties and Benders-SQP algorithms," Computational Optimization and Applications, Springer, vol. 51(1), pages 77-123, January.
    13. Tonbari, Mohamed El & Ahmed, Shabbir, 2023. "Consensus-based Dantzig-Wolfe decomposition," European Journal of Operational Research, Elsevier, vol. 307(3), pages 1441-1456.
    14. Yuning Jiang & Dimitris Kouzoupis & Haoyu Yin & Moritz Diehl & Boris Houska, 2021. "Decentralized Optimization Over Tree Graphs," Journal of Optimization Theory and Applications, Springer, vol. 189(2), pages 384-407, May.
    15. Alois Geyer & Michael Hanke & Alex Weissensteiner, 2009. "A stochastic programming approach for multi-period portfolio optimization," Computational Management Science, Springer, vol. 6(2), pages 187-208, May.
    16. Panos Parpas & Berç Rustem, 2007. "Computational Assessment of Nested Benders and Augmented Lagrangian Decomposition for Mean-Variance Multistage Stochastic Problems," INFORMS Journal on Computing, INFORMS, vol. 19(2), pages 239-247, May.
    17. Jie Sun & Xinwei Liu, 2006. "Scenario Formulation of Stochastic Linear Programs and the Homogeneous Self-Dual Interior-Point Method," INFORMS Journal on Computing, INFORMS, vol. 18(4), pages 444-454, November.
    18. Jacek Gondzio & Andreas Grothey, 2007. "Parallel interior-point solver for structured quadratic programs: Application to financial planning problems," Annals of Operations Research, Springer, vol. 152(1), pages 319-339, July.
    19. Miguel, Angel Víctor de & Nogales Martín, Francisco Javier, 2004. "On the relationship between bilevel decomposition algorithms and direct interior-point methods," DES - Working Papers. Statistics and Econometrics. WS ws042509, Universidad Carlos III de Madrid. Departamento de Estadística.
    20. Xi Yang & Jacek Gondzio & Andreas Grothey, 2010. "Asset liability management modelling with risk control by stochastic dominance," Journal of Asset Management, Palgrave Macmillan, vol. 11(2), pages 73-93, June.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:inm:orijoc:v:29:y:2017:i:4:p:612-630. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.