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Linear multistep methods for optimal control problems and applications to hyperbolic relaxation systems

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  • Albi, G.
  • Herty, M.
  • Pareschi, L.

Abstract

We are interested in high-order linear multistep schemes for time discretization of adjoint equations arising within optimal control problems. First we consider optimal control problems for ordinary differential equations and show loss of accuracy for Adams–Moulton and Adams–Bashforth methods, whereas BDF methods preserve high-order accuracy. Subsequently we extend these results to semi-Lagrangian discretizations of hyperbolic relaxation systems. Computational results illustrate theoretical findings.

Suggested Citation

  • Albi, G. & Herty, M. & Pareschi, L., 2019. "Linear multistep methods for optimal control problems and applications to hyperbolic relaxation systems," Applied Mathematics and Computation, Elsevier, vol. 354(C), pages 460-477.
    • Handle: RePEc:eee:apmaco:v:354:y:2019:i:c:p:460-477
    DOI: 10.1016/j.amc.2019.02.021
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    References listed on IDEAS

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    1. Elisabetta Carlini & Adriano Festa & Francisco J. Silva & Marie-Therese Wolfram, 2017. "A Semi-Lagrangian Scheme for a Modified Version of the Hughes’ Model for Pedestrian Flow," Dynamic Games and Applications, Springer, vol. 7(4), pages 683-705, December.
    2. Alina Chertock & Michael Herty & Alexander Kurganov, 2014. "An Eulerian–Lagrangian method for optimization problems governed by multidimensional nonlinear hyperbolic PDEs," Computational Optimization and Applications, Springer, vol. 59(3), pages 689-724, December.
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    Cited by:

    1. Jens Lang & Bernhard A. Schmitt, 2024. "Implicit Peer Triplets in Gradient-Based Solution Algorithms for ODE Constrained Optimal Control," Journal of Optimization Theory and Applications, Springer, vol. 203(1), pages 985-1026, October.

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