William W. Hager

An O(1/k) Convergence Rate for the Variable Stepsize Bregman Operator Splitting Algorithm

  • William W. Hager
  • Maryam Yashtini
  • Hongchao Zhang
    • Categories Nonsmooth Optimization Tags , , , , ,

    An earlier paper proved the convergence of a variable stepsize Bregman operator splitting algorithm (BOSVS) for minimizing $\phi(Bu)+H(u)$ where $H$ and $\phi$ are convex functions, and $\phi$ is possibly nonsmooth. The algorithm was shown to be relatively efficient when applied to partially parallel magnetic resonance image reconstruction problems. In this paper, the convergence rate of … Read more

    An efficient gradient method using the Yuan steplength

  • Roberta De Asmundis
  • Daniela di Serafino
  • William W. Hager
  • Gerardo Toraldo
  • Hongchao Zhang
    • Categories Nonlinear Optimization, Quadratic Programming, Unconstrained Optimization Tags , ,

    We propose a new gradient method for quadratic programming, named SDC, which alternates some SD iterates with some gradient iterates that use a constant steplength computed through the Yuan formula. The SDC method exploits the asymptotic spectral behaviour of the Yuan steplength to foster a selective elimination of the components of the gradient along the … Read more