We consider an elliptic optimal control problem with a control in the space of regular Borel measures. The Tikhonov regularization term is given by the Wasserstein-$p$-distance , $p \in [1, \infty)$, to a given prior. We establish first-order necessary optimality conditions using the convex subdifferential of the Wasserstein-$p$-distance. These conditions couple the adjoint state with the...
This talk deals with an optimal control problem, where the state variable is given as a parametrized balanced viscosity solution of a rate-independent system with non convex energy.
Under certain assumptions on the data one can prove the existence of globally optimal solutions for external loads in $H^1(0,T)$.
Moreover, we investigate the approximability of optimal solutions by viscous...
We consider optimal control problems where the control acts in the coefficient of the main part of the elliptic differential operator. We develop expansions of the cost functional with respect to perturbations of the control by characteristic functions. In comparison to standard Frechet derivatives in $L^\infty$, an additional term appears, which is related to the so-called polarization...
In this talk, we are concerned with model order reduction in the context of iterative regularization methods for the solution of inverse problems arising from parameter identification in elliptic partial differential equations. Such methods typically require a large number of forward solutions, which makes the use of the reduced basis method attractive to reduce computational complexity....
We consider a least squares formulation of a linear parabolic equation in spaces with natural regularity. As a consequence the formulation contains the Riesz isomorphism.
The discrete approach uses space-time finite elements and a suitable approximation of the Riesz isomorphism. Using finite elements that are separable with respect to space and time
the final fully discrete representation...
This talk presents recent results on the SQP method for hyperbolic PDE-constrained optimization in acoustic full waveform inversion. The analysis of the SQP method is mainly challenging due to the involved hyperbolicity and second-order bilinear structure. This notorious character leads to undesired effects of regularity loss in the SQP iteration calling for a substantial extension of...
Image registration is crucial in many imaging applications such as medical imaging or computer vision. The goal of finding a suitable transformation between two images poses similar restrictions and requirements on the set of admissible transformations as shape optimization problems. In the scope of this talk, we build on an approach that models image registration as an optimization problem...
In this talk, we analyze optimal control problems for quasilinear strictly hyperbolic systems of conservation laws where the control is the initial state of the system. The problem is of interest, for example, in the context of fluid mechanics or traffic flow modelling. Similar problems for scalar conservation laws have already been studied. However, the case of hyperbolic systems is more...
We derive and present error estimates for numerical approximations of a particular Clarke subgradient for reduced objective functions arising in the optimal control of the obstacle problem. The corresponding generalized derivative of the solution operator of the obstacle problem is a solution operator of a Dirichlet problem on the complement of the strictly active set. Using finite element...
In electric machine design efficient methods for the optimization of geometry and associated parameters are essential. Nowadays, it is necessary to handle uncertainty caused by manufacturing or material tolerances. In this work we propose a robust optimization approach to handle uncertainty in the design of a 3-phase, 6-pole Permanent Magnet Synchronous Motor (PMSM). The geometry is...
In this talk, we consider the introduction of a control variable into
the coefficients of the variational inequality constraint of an
optimal control problem. To this effect, we discuss optimality
conditions for a problem governed by an obstacle problem with control in the coefficients.
Since the obstacle problem acts as a complementarity constraint, it is known, that standard constraint...
