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A measure space approach to optimal source placement

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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.

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Acknowledgements

This work was supported by the Austrian Science Fund (FWF) under grant SFB F32 (SFB “Mathematical Optimization and Applications in Biomedical Sciences”). The authors wish to thank Patricia Brunner, Manuel Freiberger and Hermann Scharfetter of the Institute of Medical Engineering, Graz University of Technology, for their help on the photochemotherapy example.

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  1. Institute for Mathematics and Scientific Computing, University of Graz, Graz, Austria

    Christian Clason & Karl Kunisch

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  1. Christian Clason
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  2. Karl Kunisch
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Correspondence to Christian Clason.

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Clason, C., Kunisch, K. A measure space approach to optimal source placement. Comput Optim Appl 53, 155–171 (2012). https://doi.org/10.1007/s10589-011-9444-9

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