Titlebook: Control and Optimization with PDE Constraints; Kristian Bredies,Christian Clason,Gregory Winckel Book 2013 Springer Basel 2013 PDE-constra

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Parareal in Time Intermediate Targets Methods for Optimal Control Problems,tion. Our approach is based on an iterative update of a sequence of intermediate targets that gives rise to independent sub-problems that can be solved in parallel. This method can be coupled with the parareal in time algorithm. Numerical experiments show the efficiency of our method.

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,Hamilton–Jacobi–Bellman Equations on Multi-domains, While the notion of viscosity solution is by now well known, the question of uniqueness of solution, when the Hamiltonian is discontinuous, remains an important issue. A uniqueness result has been derived for a class of problems, where the behavior of the solution, in the region of discontinuity of

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Gradient Computation for Model Calibration with Pointwise Observations,ptimization problem with PDE constraints and usually pointwise observations in the objective function. Thus, the adjoint equation of this problem involves Dirac delta functions and needs a special treatment from a numerical point of view. We show by means of numerical results that also the order of

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