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Inexact Restoration for Euler Discretization of Box-Constrained Optimal Control Problems

Author

Listed:
  • Nahid Banihashemi

    (University of South Australia)

  • C. Yalçın Kaya

    (University of South Australia)

Abstract

The Inexact Restoration method for Euler discretization of state and control constrained optimal control problems is studied. Convergence of the discretized (finite-dimensional optimization) problem to an approximate solution using the Inexact Restoration method and convergence of the approximate solution to a continuous-time solution of the original problem are established. It is proved that a sufficient condition for convergence of the Inexact Restoration method is guaranteed to hold for the constrained optimal control problem. Numerical experiments employing the modelling language AMPL and optimization software Ipopt are carried out to illustrate the robustness of the Inexact Restoration method by means of two computationally challenging optimal control problems, one involving a container crane and the other a free-flying robot. The experiments interestingly demonstrate that one might be better-off using Ipopt as part of the Inexact Restoration method (in its subproblems) rather than using Ipopt directly on its own.

Suggested Citation

  • Nahid Banihashemi & C. Yalçın Kaya, 2013. "Inexact Restoration for Euler Discretization of Box-Constrained Optimal Control Problems," Journal of Optimization Theory and Applications, Springer, vol. 156(3), pages 726-760, March.
    • Handle: RePEc:spr:joptap:v:156:y:2013:i:3:d:10.1007_s10957-012-0140-4
    DOI: 10.1007/s10957-012-0140-4
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    References listed on IDEAS

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    1. Andreas Fischer & Ana Friedlander, 2010. "A new line search inexact restoration approach for nonlinear programming," Computational Optimization and Applications, Springer, vol. 46(2), pages 333-346, June.
    2. C. Y. Kaya & J. M. Martínez, 2007. "Euler Discretization and Inexact Restoration for Optimal Control," Journal of Optimization Theory and Applications, Springer, vol. 134(2), pages 191-206, August.
    3. R. Pytlak & R. B. Vinter, 1999. "Feasible Direction Algorithm for Optimal Control Problems with State and Control Constraints: Implementation," Journal of Optimization Theory and Applications, Springer, vol. 101(3), pages 623-649, June.
    4. Juliano Francisco & J. Martínez & Leandro Martínez & Feodor Pisnitchenko, 2011. "Inexact restoration method for minimization problems arising in electronic structure calculations," Computational Optimization and Applications, Springer, vol. 50(3), pages 555-590, December.
    5. R. Andreani & S. Castro & J. Chela & A. Friedlander & S. Santos, 2009. "An inexact-restoration method for nonlinear bilevel programming problems," Computational Optimization and Applications, Springer, vol. 43(3), pages 307-328, July.
    6. C.Y. Kaya & J.L. Noakes, 2003. "Computational Method for Time-Optimal Switching Control," Journal of Optimization Theory and Applications, Springer, vol. 117(1), pages 69-92, April.
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    Cited by:

    1. C. Kaya & Helmut Maurer, 2014. "A numerical method for nonconvex multi-objective optimal control problems," Computational Optimization and Applications, Springer, vol. 57(3), pages 685-702, April.
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    4. Regina S. Burachik & Alexander C. Kalloniatis & C. Yalçın Kaya, 2021. "Sparse Network Optimization for Synchronization," Journal of Optimization Theory and Applications, Springer, vol. 191(1), pages 229-251, October.
    5. E. G. Birgin & L. F. Bueno & J. M. Martínez, 2016. "Sequential equality-constrained optimization for nonlinear programming," Computational Optimization and Applications, Springer, vol. 65(3), pages 699-721, December.

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