SPEAKER: Daniel Walter (HU Berlin)
Title: A generalized conditional gradient method for infinite-dimensional nonsmooth optimization
Abstract:
Nonsmooth regularizers have become a cornerstone of modern inverse problem and optimal control theory. This is attributed to the observation that a suitable choice of the penalty function brings forth desired structural features in the solution of the associated minimization problems. We propose a novel accelerated generalized conditional gradient method for problems involving nonsmooth regularization terms over infinite dimensional function spaces. The algorithm relies on the mutual update of an active set~$mathcal{A}_k$ of extremal points of the unit ball of the regularizer and of an iterate~$u_k$ in its conic hull. Imposing additional assumptions on the dual variables, its asymptotic linear convergence is shown. The proof relies on two key observations: First, the equivalence of the considered problem to the minimization of a lifted functional over a particular space of Radon measures using Choquet's theorem. Second, we connect the new algorithm to a Primal-Dual-Active-point Method on the lifted problem for which we finally derive the desired convergence rates.
Date: 2 May 2023, Place: Zilverling 2126, Time: 14:00-15:00
