Deren Han

Linear Rate Convergence of the Alternating Direction Method of Multipliers for Convex Composite Quadratic and Semi-Definite Programming

  • Deren Han
  • Defeng Sun
  • Liwei Zhang
    • Categories Convex and Nonsmooth Optimization, Linear, Cone and Semidefinite Programming, Nonlinear Optimization Tags , , , , ,

    In this paper, we aim to provide a comprehensive analysis on the linear rate convergence of the alternating direction method of multipliers (ADMM) for solving linearly constrained convex composite optimization problems. Under a certain error bound condition, we establish the global linear rate of convergence for a more general semi-proximal ADMM with the dual steplength … Read more

    A semi-proximal-based strictly contractive Peaceman-Rachford splitting method

  • Yan Gu
  • Deren Han
  • Bo Jiang
    • Categories Convex and Nonsmooth Optimization Tags , , , ,

    The Peaceman-Rachford splitting method is very efficient for minimizing sum of two functions each depends on its variable, and the constraint is a linear equality. However, its convergence was not guaranteed without extra requirements. Very recently, He et al. (SIAM J. Optim. 24: 1011 – 1040, 2014) proved the convergence of a strictly contractive Peaceman-Rachford … Read more

    The direct extension of ADMM for three-block separable convex minimization models is convergent when one function is strongly convex

  • Xingju Cai
  • Deren Han
  • Xiao-Ming Yuan
    • Categories Convex Optimization Tags , , ,

    The alternating direction method of multipliers (ADMM) is a benchmark for solving a two-block linearly constrained convex minimization model whose objective function is the sum of two functions without coupled variables. Meanwhile, it is known that the convergence is not guaranteed if the ADMM is directly extended to a multiple-block convex minimization model whose objective … Read more

    Convergence analysis of the Peaceman-Rachford splitting method for nonsmooth convex optimization

  • Deren Han
  • Xiao-Ming Yuan
    • Categories Convex Optimization Tags , , , ,

    In this paper, we focus on the convergence analysis for the application of the Peaceman-Rachford splitting method to a convex minimization model whose objective function is the sum of a smooth and nonsmooth convex functions. The sublinear convergence rate in term of the worst-case O(1/t) iteration complexity is established if the gradient of the smooth … Read more