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Elliptic optimal control problems with L 1 -control cost and applications for the placement of control devices

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  • Georg Stadler

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  • 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.
    • Handle: RePEc:spr:coopap:v:44:y:2009:i:2:p:159-181
    DOI: 10.1007/s10589-007-9150-9
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    1. ,, 2000. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 16(2), pages 287-299, April.
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    Cited by:

    1. Pierluigi Colli & Andrea Signori & Jürgen Sprekels, 2022. "Optimal Control Problems with Sparsity for Tumor Growth Models Involving Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 194(1), pages 25-58, July.
    2. Sergio González-Andrade & Sofía López-Ordóñez & Pedro Merino, 2021. "Nonsmooth exact penalization second-order methods for incompressible bi-viscous fluids," Computational Optimization and Applications, Springer, vol. 80(3), pages 979-1025, December.
    3. D. Hafemeyer & F. Mannel, 2022. "A path-following inexact Newton method for PDE-constrained optimal control in BV," Computational Optimization and Applications, Springer, vol. 82(3), pages 753-794, July.
    4. Roland Herzog & Johannes Obermeier & Gerd Wachsmuth, 2015. "Annular and sectorial sparsity in optimal control of elliptic equations," Computational Optimization and Applications, Springer, vol. 62(1), pages 157-180, September.
    5. 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.
    6. 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.
    7. Michael Hintermüller & Tao Wu, 2014. "A superlinearly convergent R-regularized Newton scheme for variational models with concave sparsity-promoting priors," Computational Optimization and Applications, Springer, vol. 57(1), pages 1-25, January.
    8. Eduardo Casas & Mariano Mateos & Arnd Rösch, 2018. "Improved approximation rates for a parabolic control problem with an objective promoting directional sparsity," Computational Optimization and Applications, Springer, vol. 70(1), pages 239-266, May.
    9. 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.
    10. Xiaoliang Song & Bo Chen & Bo Yu, 2018. "An efficient duality-based approach for PDE-constrained sparse optimization," Computational Optimization and Applications, Springer, vol. 69(2), pages 461-500, March.
    11. Pedro Merino, 2019. "A difference-of-convex functions approach for sparse PDE optimal control problems with nonconvex costs," Computational Optimization and Applications, Springer, vol. 74(1), pages 225-258, September.
    12. J. C. De Los Reyes & E. Loayza & P. Merino, 2017. "Second-order orthant-based methods with enriched Hessian information for sparse $$\ell _1$$ ℓ 1 -optimization," Computational Optimization and Applications, Springer, vol. 67(2), pages 225-258, June.
    13. Christian Clason & Karl Kunisch, 2012. "A measure space approach to optimal source placement," Computational Optimization and Applications, Springer, vol. 53(1), pages 155-171, September.
    14. Richard C. Barnard & Christian Clason, 2017. "$$L^1$$ L 1 penalization of volumetric dose objectives in optimal control of PDEs," Computational Optimization and Applications, Springer, vol. 67(2), pages 401-419, June.
    15. Xiaotong Chen & Xiaoliang Song & Zixuan Chen & Lijun Xu, 2023. "A Multilevel Heterogeneous ADMM Algorithm for Elliptic Optimal Control Problems with L 1 -Control Cost," Mathematics, MDPI, vol. 11(3), pages 1-21, January.
    16. Christian Clason & Thi Bich Tram Do & Frank Pörner, 2018. "Error estimates for the approximation of multibang control problems," Computational Optimization and Applications, Springer, vol. 71(3), pages 857-878, December.
    17. Mariano Mateos, 2021. "Sparse Dirichlet optimal control problems," Computational Optimization and Applications, Springer, vol. 80(1), pages 271-300, September.
    18. Samuel Amstutz & Antoine Laurain, 2013. "A semismooth Newton method for a class of semilinear optimal control problems with box and volume constraints," Computational Optimization and Applications, Springer, vol. 56(2), pages 369-403, October.
    19. Mattia Bongini & Massimo Fornasier & Francesco Rossi & Francesco Solombrino, 2017. "Mean-Field Pontryagin Maximum Principle," Journal of Optimization Theory and Applications, Springer, vol. 175(1), pages 1-38, October.
    20. Malte Braack & Martin F. Quaas & Benjamin Tews & Boris Vexler, 2018. "Optimization of Fishing Strategies in Space and Time as a Non-convex Optimal Control Problem," Journal of Optimization Theory and Applications, Springer, vol. 178(3), pages 950-972, September.
    21. Li, Hongyi & Wang, Chaojie & Zhao, Di, 2020. "Preconditioning for PDE-constrained optimization with total variation regularization," Applied Mathematics and Computation, Elsevier, vol. 386(C).
    22. Francisco Fuica & Felipe Lepe & Enrique Otárola & Daniel Quero, 2023. "An Optimal Control Problem for the Navier–Stokes Equations with Point Sources," Journal of Optimization Theory and Applications, Springer, vol. 196(2), pages 590-616, February.

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