joint work with Jørgen Dokken, Sebastian Mitusch
Shape-derivatives combined with the adjoint approach offer an efficient approach for solving shape optimisation problems, but their derivation is error-prone especially for complex PDEs. In this talk, we present an algorithmic differentiation tool that automatically computes shape derivatives by exploiting the symbolic representation of variational problems in the finite element framework FEniCS. We demonstrate that our approach computes first and second order shape derivatives for a wide range of PDEs and functionals, approaches optimal performance and works naturally in parallel.
joint work with Boris Vexler
This talk is concerned with parabolic optimal control problems that involve pointwise state constraints. We show that, if the bound in the state constraint satisfies a suitable compatibility condition, then optimal controls enjoy L^oo(L^2), L^2(H^1) and (with a suitable Banach space Y) BV(Y^*)-regularity. In contrast to classical approaches, our analysis requires neither a Slater point nor additional control constraints nor assumptions on the spatial dimension nor smoothness of the objective function.
joint work with Maria Soledad Aronna, Frederic Bonnans
In this talk we consider an optimal control problem governed by a semilinear heat equation with bilinear control-state terms and subject to control and state constraints. The state constraints are of integral-type, the integral being with respect to the space variable. The control is multidimensional. The cost functional is of a tracking-type and contains a linear term in the control variables. We derive second order necessary and sufficient conditions relying on the Goh transformation, the concept of alternative costates, and quasi-radial critical directions.