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Efficient parallel solution of large-scale nonlinear dynamic optimization problems

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  • Daniel Word
  • Jia Kang
  • Johan Akesson
  • Carl Laird

Abstract

This paper presents a decomposition strategy applicable to DAE constrained optimization problems. A common solution method for such problems is to apply a direct transcription method and solve the resulting nonlinear program using an interior-point algorithm. For this approach, the time to solve the linearized KKT system at each iteration typically dominates the total solution time. In our proposed method, we exploit the structure of the KKT system resulting from a direct collocation scheme for approximating the DAE constraints in order to compute the necessary linear algebra operations on multiple processors. This approach is applied to find the optimal control profile of a combined cycle power plant with promising results on both distributed memory and shared memory computing architectures with speedups of over 50 times possible. Copyright Springer Science+Business Media New York 2014

Suggested Citation

  • Daniel Word & Jia Kang & Johan Akesson & Carl Laird, 2014. "Efficient parallel solution of large-scale nonlinear dynamic optimization problems," Computational Optimization and Applications, Springer, vol. 59(3), pages 667-688, December.
    • Handle: RePEc:spr:coopap:v:59:y:2014:i:3:p:667-688
    DOI: 10.1007/s10589-014-9651-2
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    References listed on IDEAS

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    1. C. V. Rao & S. J. Wright & J. B. Rawlings, 1998. "Application of Interior-Point Methods to Model Predictive Control," Journal of Optimization Theory and Applications, Springer, vol. 99(3), pages 723-757, December.
    2. Eligius M. T. Hendrix & Boglárka G.-Tóth, 2010. "Nonlinear Programming algorithms," Springer Optimization and Its Applications, in: Introduction to Nonlinear and Global Optimization, chapter 5, pages 91-136, Springer.
    3. Victor DeMiguel & Francisco J. Nogales, 2008. "On Decomposition Methods for a Class of Partially Separable Nonlinear Programs," Mathematics of Operations Research, INFORMS, vol. 33(1), pages 119-139, February.
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    Cited by:

    1. Begüm Şenses Cannataro & Anil V. Rao & Timothy A. Davis, 2016. "State-defect constraint pairing graph coarsening method for Karush–Kuhn–Tucker matrices arising in orthogonal collocation methods for optimal control," Computational Optimization and Applications, Springer, vol. 64(3), pages 793-819, July.
    2. Jose S. Rodriguez & Robert B. Parker & Carl D. Laird & Bethany L. Nicholson & John D. Siirola & Michael L. Bynum, 2023. "Scalable Parallel Nonlinear Optimization with PyNumero and Parapint," INFORMS Journal on Computing, INFORMS, vol. 35(2), pages 509-517, March.
    3. Bethany L. Nicholson & Wei Wan & Shivakumar Kameswaran & Lorenz T. Biegler, 2018. "Parallel cyclic reduction strategies for linear systems that arise in dynamic optimization problems," Computational Optimization and Applications, Springer, vol. 70(2), pages 321-350, June.

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