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Optimization techniques for tree-structured nonlinear problems

Author

Listed:
  • Jens Hübner

    (HaCon Ingenieurgesellschaft mbH)

  • Martin Schmidt

    (Trier University)

  • Marc C. Steinbach

    (Leibniz Universität Hannover)

Abstract

Robust model predictive control approaches and other applications lead to nonlinear optimization problems defined on (scenario) trees. We present structure-preserving Quasi-Newton update formulas as well as structured inertia correction techniques that allow to solve these problems by interior-point methods with specialized KKT solvers for tree-structured optimization problems. The same type of KKT solvers could be used in active-set based SQP methods. The viability of our approach is demonstrated by two robust control problems.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:comgts:v:17:y:2020:i:3:d:10.1007_s10287-020-00362-9
    DOI: 10.1007/s10287-020-00362-9
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. Tamra J. Carpenter & Irvin J. Lustig & John M. Mulvey & David F. Shanno, 1993. "Separable Quadratic Programming via a Primal-Dual Interior Point Method and its Use in a Sequential Procedure," INFORMS Journal on Computing, INFORMS, vol. 5(2), pages 182-191, May.
    6. Joseph Czyzyk & Robert Fourer & Sanjay Mehrotra, 1995. "A Study of the Augmented System and Column-Splitting Approaches for Solving Two-Stage Stochastic Linear Programs by Interior-Point Methods," INFORMS Journal on Computing, INFORMS, vol. 7(4), pages 474-490, November.
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    Cited by:

    1. Toly Chen, 2021. "A diversified AHP-tree approach for multiple-criteria supplier selection," Computational Management Science, Springer, vol. 18(4), pages 431-453, October.

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