inertial

Relative-error inertial-relaxed inexact versions of Douglas-Rachford and ADMM splitting algorithms

  • M. Marques Alves
  • Jonathan Eckstein
  • Jefferson Gonçalves Melo
  • Marina Geremia
    • Categories Convex and Nonsmooth Optimization Tags , , , , ,

    This paper derives new inexact variants of the Douglas-Rachford splitting method for maximal monotone operators and the alternating direction method of multipliers (ADMM) for convex optimization. The analysis is based on a new inexact version of the proximal point algorithm that includes both an inertial step and overrelaxation. We apply our new inexact ADMM method … Read more

    On inexact relative-error hybrid proximal extragradient, forward-backward and Tseng’s modified forward-backward methods with inertial effects

  • M. Marques Alves
  • Raul T. Marcavillaca
    • Categories Convex and Nonsmooth Optimization Tags , , , , , , , ,

    In this paper, we propose and study the asymptotic convergence and nonasymptotic global convergence rates (iteration-complexity) of an inertial under-relaxed version of the relative-error hybrid proximal extragradient (HPE) method for solving monotone inclusion problems. We analyze the proposed method under more flexible assumptions than existing ones on the extrapolation and relative-error parameters. As applications, we … Read more