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Solving inverse optimal control problems via value functions to global optimality

Author

Listed:
  • Stephan Dempe

    (Technische Universität Bergakademie Freiberg)

  • Felix Harder

    (Brandenburgische Technische Universität Cottbus-Senftenberg)

  • Patrick Mehlitz

    (Brandenburgische Technische Universität Cottbus-Senftenberg)

  • Gerd Wachsmuth

    (Brandenburgische Technische Universität Cottbus-Senftenberg)

Abstract

In this paper, we show how a special class of inverse optimal control problems of elliptic partial differential equations can be solved globally. Using the optimal value function of the underlying parametric optimal control problem, we transfer the overall hierarchical optimization problem into a nonconvex single-level one. Unfortunately, standard regularity conditions like Robinson’s CQ are violated at all the feasible points of this surrogate problem. It is, however, shown that locally optimal solutions of the problem solve a Clarke-stationarity-type system. Moreover, we relax the feasible set of the surrogate problem iteratively by approximating the lower level optimal value function from above by piecewise affine functions. This allows us to compute globally optimal solutions of the original inverse optimal control problem. The global convergence of the resulting algorithm is shown theoretically and illustrated by means of a numerical example.

Suggested Citation

  • Stephan Dempe & Felix Harder & Patrick Mehlitz & Gerd Wachsmuth, 2019. "Solving inverse optimal control problems via value functions to global optimality," Journal of Global Optimization, Springer, vol. 74(2), pages 297-325, June.
    • Handle: RePEc:spr:jglopt:v:74:y:2019:i:2:d:10.1007_s10898-019-00758-1
    DOI: 10.1007/s10898-019-00758-1
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    References listed on IDEAS

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    1. S. Dempe & S. Franke, 2016. "On the solution of convex bilevel optimization problems," Computational Optimization and Applications, Springer, vol. 63(3), pages 685-703, April.
    2. R. Horst & N. V. Thoai, 1999. "DC Programming: Overview," Journal of Optimization Theory and Applications, Springer, vol. 103(1), pages 1-43, October.
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    Cited by:

    1. Markus Friedemann & Felix Harder & Gerd Wachsmuth, 2023. "Finding global solutions of some inverse optimal control problems using penalization and semismooth Newton methods," Journal of Global Optimization, Springer, vol. 86(4), pages 1025-1061, August.
    2. Abdelmajid El Hakoume & Amine Laghrib & Aissam Hadri & Lekbir Afraites, 2023. "An Optimal Fluid Optical Flow Registration for Super-resolution with Lamé Parameters Learning," Journal of Optimization Theory and Applications, Springer, vol. 197(2), pages 508-538, May.
    3. Majid E. Abbasov, 2023. "Finding the set of global minimizers of a piecewise affine function," Journal of Global Optimization, Springer, vol. 85(1), pages 1-13, January.

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