Proximal methods for point source localisation

Point source localisation is generally modelled as a Lasso-type problem on measures. However, optimisation methods in non-Hilbert spaces, such the space of Radon measures, are much less developed than Hilbert spaces. Most numerical algorithms for point based Frank-Wolfe conditional gradient method, which ad hoc convergence theory developed. We develop extensions proximal-type to spaces This includes forward-backward splitting, its inertial version, and primal-dual proximal splitting. Their proofs follow standard patterns. demonstrate their efficacy.