A precise characterization of the extremal points of sublevel sets of nonsmooth penalties
provides both detailed information about minimizers, and optimality conditions in general …

We propose a fast and scalable polyatomic Frank-Wolfe (P-FW) algorithm for the resolution
of high-dimensional LASSO regression problems. This algorithm improves upon traditional …

We study measure-valued solutions of the inhomogeneous continuity equation∂ t ρ t+ div (v
ρ t)= g ρ t where the coefficients v and g are of low regularity. A new superposition principle …

The total generalized variation (TGV) is a popular regularizer in inverse problems and
imaging combining discontinuous solutions and higher order smoothing. In particular …

In this note, we provide a characterization for the set of extreme points of the Lipschitz unit
ball in a specific vectorial setting. While the analysis of the case of real-valued functions is …

My biggest achievement with this thesis is earning the respect of my professor, colleagues,
and friends. I sincerely thank everyone I have worked with for the scientific discussions. I feel …