Maïtine Bergounioux

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In this paper we investigate optimal control problems governed by elliptic variational inequalities with additional state constraints. We present a relaxed formulation for the problem. With penalization methods and approximation techniques we give qualification conditions to get first-order optimality conditions. 1. Introduction. In this paper we(More)
This paper deals with a method of tomographic reconstruction of radially symmetric objects from a single radiograph, in order to study the behavior of shocked material. The usual tomographic reconstruction algorithms such as generalized inverse or filtered back-projection cannot be applied here because data are very noisy and the inverse problem associated(More)
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)
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)