finite activity identification

Local Convergence Properties of Douglas–Rachford and ADMM

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

    The Douglas–Rachford (DR) and alternating direction method of multipliers (ADMM) are two proximal splitting algorithms designed to minimize the sum of two proper lower semi-continuous convex functions whose proximity operators are easy to compute. The goal of this work is to understand the local linear convergence behaviour of DR/ADMM when the involved functions are moreover … Read more

    Activity Identification and Local Linear Convergence of Douglas-Rachford/ADMM under Partial Smoothness

  • Jalal Fadili
  • Jingwei Liang
  • Russell Luke
  • Gabriel Peyré
    • Categories Convex and Nonsmooth Optimization, Convex Optimization, Nonsmooth Optimization Tags , , , ,

    Proximal splitting algorithms are becoming popular to solve convex optimization problems in variational image processing. Within this class, Douglas-Rachford (DR) and ADMM are designed to minimize the sum of two proper lower semicontinuous convex functions whose proximity operators are easy to compute. The goal of this work is to understand the local convergence behaviour of … Read more