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Abstract. This article presents a numerical method for approximation of some optimal control problems for partial differential equations. The method uses regularization derived from consistency with the corresponding Hamilton-Jacobi-Bellman equations in infinite dimension. In particular, optimal designs of elastic structures such as distributing a limited amount of material to min-imize its compliance, or to detect interior material distributions from surface measurements, are computed. The derived Pontryagin based method pre-sented here is simple to use with standard PDE-software using Newton itera