State constrained optimal control problems represent severe analytical and numerical challenges. A numerical algorithm based on an active set strategy involving primal as well as dual variables, suggested by a generalized Moreau-Yosida regularization of the state constraint is proposed and analyzed. Numerical examples are included.
We consider an optimal control problem where the state satisfies a bilateral elliptic varia-tional inequality and the control functions are the upper and lower obstacles. We seek a state that is close to a desired profile and the H 2 norms of the obstacles are not too large. Existence results are given and an optimality system is derived. A particular case… (More)
We consider an optimal control where the state-control relation is given by a quasi-variational inequality, namely a generalized obstacle problem. We give an existence result for solutions to such a problem. The main tool is a stability result, based on the Mosco-convergence theory, that gives the weak closeness of the control-to-state operator. We end the… (More)
The aim of this paper is to construct a model which decomposes a 3D image into two components: the first one containing the geometrical structure of the image, the second one containing the noise. The proposed method is based on a second order variational model and an undecimated wavelet thresholding operator. The numerical implementation is described, and… (More)