proximal splitting

Iteration-Complexity of a Generalized Forward Backward Splitting Algorithm

  • Jalal Fadili
  • Jingwei Liang
  • Gabriel Peyré
    • Categories Convex Optimization Tags , , ,

    In this paper, we analyze the iteration-complexity of a generalized forward-backward (GFB) splitting algorithm, recently proposed in~\cite{gfb2011}, for minimizing the large class of composite objectives $f + \sum_{i=1}^n h_i$ on a Hilbert space, where $f$ has a Lipschitz-continuous gradient and the $h_i$’s are simple (i.e. whose proximity operator is easily computable ). We derive iteration-complexity … Read more

    Generalized Forward-Backward Splitting

  • Jalal Fadili
  • Hugo Raguet
  • Gabriel Peyré
    • Categories Convex Optimization, Nonsmooth Optimization Tags , , , , ,

    This paper introduces the generalized forward-backward splitting algorithm for minimizing convex functions of the form $F + \sum_{i=1}^n G_i$, where $F$ has a Lipschitz-continuous gradient and the $G_i$’s are simple in the sense that their Moreau proximity operators are easy to compute. While the forward-backward algorithm cannot deal with more than $n = 1$ non-smooth … Read more