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A measure space approach to optimal source placement

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  • Christian Clason

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  • Karl Kunisch

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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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    File URL: http://hdl.handle.net/10.1007/s10589-011-9444-9
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    References listed on IDEAS

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    1. A. Meltzer & Peter Ordeshook & Thomas Romer, 1983. "Introduction," Public Choice, Springer, vol. 41(1), pages 1-5, January.
    2. A. P. Thirlwall, 1983. "Introduction," Journal of Post Keynesian Economics, Taylor & Francis Journals, vol. 5(3), pages 341-344, March.
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    Cited by:

    1. 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.
    2. Michael Hinterm├╝ller & Tao Wu, 2014. "A superlinearly convergent R-regularized Newton scheme for variational models with concave sparsity-promoting priors," Computational Optimization and Applications, Springer, pages 1-25.

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