Variable Metric Forward-Backward Splitting with Applications to Monotone Inclusions in Duality

Patrick L. Combettes, Bang C. Vũ

Published 2012-06-28Version 1

We propose a variable metric forward-backward splitting algorithm and prove its convergence in real Hilbert spaces. We then use this framework to derive primal-dual splitting algorithms for solving various classes of monotone inclusions in duality. Some of these algorithms are new even when specialized to the fixed metric case. Various applications are discussed.