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

Patrick Louis Combettes (1) , Bang Cong Vu (2)

1 UPMC - Université Pierre et Marie Curie - Paris 6
2 UniGe - Università degli studi di Genova = University of Genoa

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.

Mots clés: cocoercive operator; composite operator; demiregularity; duality; forward-backward splitting algorithm; monotone inclusion; monotone operator; primal-dual algorithm; quasi-Fejér se-quence; variable metric Mathematics Subject Classifications (2010) 47H05; 49M29; 49M27; 90C25

Domaines: Optimisation et contrôle [math.OC]

Patrick Louis Combettes, Bang Cong Vu. Variable metric forward–backward splitting with applications to monotone inclusions in duality. Optimization, 2014, 63, pp.1289 - 1318. ⟨10.1080/02331934.2012.733883⟩. ⟨hal-01076989⟩