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Infinite Horizon Sparse Optimal Control

Author

Listed:
  • Dante Kalise

    (Austrian Academy of Sciences)

  • Karl Kunisch

    (Austrian Academy of Sciences
    University of Graz)

  • Zhiping Rao

    (Austrian Academy of Sciences)

Abstract

A class of infinite horizon optimal control problems involving nonsmooth cost functionals is discussed. The existence of optimal controls is studied for both the convex case and the nonconvex case, and the sparsity structure of the optimal controls promoted by the nonsmooth penalties is analyzed. A dynamic programming approach is proposed to numerically approximate the corresponding sparse optimal controllers.

Suggested Citation

  • Dante Kalise & Karl Kunisch & Zhiping Rao, 2017. "Infinite Horizon Sparse Optimal Control," Journal of Optimization Theory and Applications, Springer, vol. 172(2), pages 481-517, February.
    • Handle: RePEc:spr:joptap:v:172:y:2017:i:2:d:10.1007_s10957-016-1016-9
    DOI: 10.1007/s10957-016-1016-9
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    References listed on IDEAS

    as
    1. Eduardo Casas & Mariano Mateos, 2012. "Numerical approximation of elliptic control problems with finitely many pointwise constraints," Computational Optimization and Applications, Springer, vol. 51(3), pages 1319-1343, April.
    2. Georg Stadler, 2009. "Elliptic optimal control problems with L 1 -control cost and applications for the placement of control devices," Computational Optimization and Applications, Springer, vol. 44(2), pages 159-181, November.
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    Cited by:

    1. Daria Ghilli & Karl Kunisch, 2019. "On a Monotone Scheme for Nonconvex Nonsmooth Optimization with Applications to Fracture Mechanics," Journal of Optimization Theory and Applications, Springer, vol. 183(2), pages 609-641, November.
    2. Francesca C. Chittaro & Laura Poggiolini, 2019. "Strong Local Optimality for Generalized L1 Optimal Control Problems," Journal of Optimization Theory and Applications, Springer, vol. 180(1), pages 207-234, January.
    3. Daria Ghilli & Karl Kunisch, 2019. "On monotone and primal-dual active set schemes for $$\ell ^p$$ ℓ p -type problems, $$p \in (0,1]$$ p ∈ ( 0 , 1 ]," Computational Optimization and Applications, Springer, vol. 72(1), pages 45-85, January.

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