joint work with Constantin Christof
In this talk, we consider second-order optimality conditions for the optimal control of the obstacle problem. In particular, we are interested in sufficient conditions which guarantee the local/global optimality of the point of interest. Our analysis extends and refines existing results from the literature. We present three counter-examples which illustrate that rather peculiar effects can occur in the analysis of second-order optimality conditions for optimal control problems governed by the obstacle problem.
joint work with Stefan Ulbrich
In this talk, we discuss differentiability properties of a general class of obstacle problems and characterize generalized derivatives from the Bouligand subdifferential of the solution operator for the obstacle problem in all points of its domain. The subgradients we obtain are determined by solution operators of Dirichlet problems on quasi-open domains. To use the derived subgradients in practice within nonsmooth optimization methods, a discretization of the obstacle problem is necessary. We investigate how the respective subgradients can be approximated in this case.
joint work with Constantin Christof
The understanding of and the techniques for dealing with non-smoothness in scalar optimization with PDEs have increased drastically over the last years. In multiobjective non-smooth optimization, however, few results are known. This talk addresses the multiobjective optimal control of a non-smooth semi-linear elliptic PDE with max-type nonlinearity. First results are focused on first order optimality condition based on multiple adjoint equations. Additionally, we discuss the numeric characterization of the Pareto front for few objectives using scalarization techniques and regularization.