1. Variable metric forward–backward splitting with applications to monotone inclusions in duality
- Author
-
Bang Công Vũ, Patrick L. Combettes, Université Pierre et Marie Curie - Paris 6 (UPMC), Universita degli studi di Genova, and Università degli studi di Genova = University of Genoa (UniGe)
- Subjects
Primal dual algorithm ,Control and Optimization ,Duality (optimization) ,Forward backward ,Monotonic function ,Management Science and Operations Research ,demiregularity ,90C25 ,Composite operator ,symbols.namesake ,primal-dual algorithm ,Applied mathematics ,Mathematics ,Discrete mathematics ,49M29 ,49M27 ,quasi-Fejér se-quence ,Applied Mathematics ,Hilbert space ,Strongly monotone ,cocoercive operator ,monotone inclusion ,Monotone polygon ,variable metric Mathematics Subject Classifications (2010) 47H05 ,monotone operator ,symbols ,duality ,forward-backward splitting algorithm ,composite operator ,[MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC] - Abstract
International audience; 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.
- Published
- 2014
- Full Text
- View/download PDF