  We consider a parabolic optimal control problem with an initial measure
control. The cost functional consists of a tracking term corresponding to the
observation of the state at final time. Instead of a regularization term in the
cost functional, we follow an approach by E. Casas and K. Kunisch and consider
a bound on the measure norm of the initial control. The variational
discretization of the problem together with the optimality conditions induce
maximal discrete sparsity of the initial control, i.e. Dirac measures in space.
We present numerical experiments to illustrate our approach.
