Variable Metric Forward-Backward Splitting with Applications to Monotone   Inclusions in Duality
  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. 
Patrick L. Combettes and Bang C. V\~u
math.OC