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A measure space approach to optimal source placement

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  • Christian Clason
  • Karl Kunisch

Abstract

The problem of optimal placement of point sources is formulated as a distributed optimal control problem with sparsity constraints. For practical relevance, partial observations as well as partial and non-negative controls need to be considered. Although well-posedness of this problem requires a non-reflexive Banach space setting, a primal-predual formulation of the optimality system can be approximated well by a family of semi-smooth equations, which can be solved by a superlinearly convergent semi-smooth Newton method. Numerical examples indicate the feasibility for optimal light source placement problems in diffusive photochemotherapy. Copyright Springer Science+Business Media, LLC 2012

Suggested Citation

  • 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.
    • Handle: RePEc:spr:coopap:v:53:y:2012:i:1:p:155-171
    DOI: 10.1007/s10589-011-9444-9
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    References listed on IDEAS

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    1. 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. 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.
    2. 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.
    3. 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.

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