Jefferson Gonçalves Melo

Iteration-Complexity of a Linearized Proximal Multiblock ADMM Class for Linearly Constrained Nonconvex Optimization Problems

  • Jefferson Gonçalves Melo
  • Renato D.C. Monteiro
    • Categories Nonlinear Optimization, Nonsmooth Optimization Tags , , ,

    This paper analyzes the iteration-complexity of a class of linearized proximal multiblock alternating direction method of multipliers (ADMM) for solving linearly constrained nonconvex optimization problems. The subproblems of the linearized ADMM are obtained by partially or fully linearizing the augmented Lagrangian with respect to the corresponding minimizing block variable. The derived complexity bounds do not … Read more

    Convergence rate bounds for a proximal ADMM with over-relaxation stepsize parameter for solving nonconvex linearly constrained problems

  • Max L. N. Gonçalves
  • Jefferson Gonçalves Melo
  • Renato D.C. Monteiro
    • Categories Convex and Nonsmooth Optimization, Nonsmooth Optimization Tags , , ,

    This paper establishes convergence rate bounds for a variant of the proximal alternating direction method of multipliers (ADMM) for solving nonconvex linearly constrained optimization problems. The variant of the proximal ADMM allows the inclusion of an over-relaxation stepsize parameter belonging to the interval (0,2). To the best of our knowledge, all related papers in the … Read more

    Extending the ergodic convergence rate of the proximal ADMM

  • Max L. N. Gonçalves
  • Jefferson Gonçalves Melo
  • Renato D.C. Monteiro
    • Categories Convex Optimization, Nonsmooth Optimization Tags , , , , , , , ,

    Pointwise and ergodic iteration-complexity results for the proximal alternating direction method of multipliers (ADMM) for any stepsize in $(0,(1+\sqrt{5})/2)$ have been recently established in the literature. In addition to giving alternative proofs of these results, this paper also extends the ergodic iteration-complexity result to include the case in which the stepsize is equal to $(1+\sqrt{5})/2$. … Read more

    Improved pointwise iteration-complexity of a regularized ADMM and of a regularized non-Euclidean HPE framework

  • Max L. N. Gonçalves
  • Jefferson Gonçalves Melo
  • Renato D.C. Monteiro
    • Categories Constrained Nonlinear Optimization, Convex Optimization Tags , , , , , , ,

    This paper describes a regularized variant of the alternating direction method of multipliers (ADMM) for solving linearly constrained convex programs. It is shown that the pointwise iteration-complexity of the new method is better than the corresponding one for the standard ADMM method and that, up to a logarithmic term, is identical to the ergodic iteration-complexity … Read more