Forward-Backward L-BFGS for large-scale nonsmooth optimization

Panos Patrinos joint work with Lorenzo Stella

Institute for Advanced Studies, Lucca, Italy

Tuesday, May 12, 2015, 11:00 - 12:00

Room 01-012, Georges-Köhler-Allee 102, Freiburg 79110, Germany

We propose forward-backward L-BFGS algorithms for nonsmooth convex composite optimization problems. These rely on the concept of Forward-Backward Envelope (FBE), a smooth function whose unconstrained minimizers are solutions to the original problem. The complexity per iteration of our algorithms is similar to the one of the proximal gradient method, which makes them suitable for large scale applications. We show that the proposed algorithms enjoy the optimal convergence rate of FISTA, but are much faster in practice. The proposed algorithms have been implemented in ForBES (FORward Backward Envelope Solver), an open-source generic solver for convex optimization problems.