A measure space approach to optimal source placement

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.