contraction

Convergence Study on the Proximal Alternating Direction Method with Larger Step Size

  • Bingsheng He
  • Feng Ma
    • Categories Convex and Nonsmooth Optimization Tags , , , ,

    The alternating direction method of multipliers (ADMM) is a popular method for the separable convex programming with linear constraints, and the proximal ADMM is its important variant. Previous studies show that the relaxation factor $\gamma\in (0, \frac{1+\sqrt{5}}{2})$ by Fortin and Glowinski for the ADMM is also valid for the proximal ADMM. In this paper, we … Read more

    On the Direct Extension of ADMM for Multi-block Separable Convex Programming and Beyond: From Variational Inequality Perspective

  • Bingsheng He
  • Xiao-Ming Yuan
    • Categories Convex Optimization Tags , , , , ,

    When the alternating direction method of multipliers (ADMM) is extended directly to a multi-block separable convex minimization model whose objective function is in form of more than two functions without coupled variables, it was recently shown that the convergence is not guaranteed. This fact urges to develop efficient algorithms that can preserve completely the numerical … Read more