Variable metric forward–backward splitting with applications to monotone inclusions in duality

This is the authors' abstract. We don't add key points for this paper.

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.