A measure space approach to optimal source placement

Authors:
Christian Clason;Karl Kunisch
Affiliations:
Institute for Mathematics and Scientific Computing, University of Graz, Graz, Austria;Institute for Mathematics and Scientific Computing, University of Graz, Graz, Austria
Venue:
Computational Optimization and Applications
Year:
2012

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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.