By Prof. Dr. Jean-francois aujol institut de mathématiques université de bordeaux, france
Seminar Date: 2023-09-05
This work is related with large scale optimization. We are interested in the famous FISTA algorithm. We show that FISTA is an automatic geometrically optimized algorithm for functions satisfying a quadratic growth assumption. This explains why FISTA works better than the standard Forward-Backward algorithm (FB) in such a case, although FISTA is known to have a polynomial asymptotical convergence rate while FB is exponential. We provide a simple rule to tune the a parameter within the FISTA algorithm to reach an e-solution with an optimal number of iterations. These new results highlight the efficiency of FISTA algorithms, and they rely on new non asymptotic bounds for FISTA. This is a joint work with Charles Dossal and Aude Rondepierre (INSA Toulouse).