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Licensed Unlicensed Requires Authentication Published by De Gruyter 2022

6 Variational discretization approach applied to an optimal control problem with bounded measure controls

From the book Optimization and Control for Partial Differential Equations

  • Evelyn Herberg and Michael Hinze


We consider a parabolic optimal control problem with 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 [6] and consider a bound on the measure norm of the initial control. The variational discretization of the problem, together with the optimality conditions, induces maximal discrete sparsity of the initial control, i. e., Dirac measures in space. We present numerical experiments to illustrate our approach.

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