Wenbo Gao

ADMM for Multiaffine Constrained Optimization

  • Frank E. Curtis
  • Wenbo Gao
  • Donald Goldfarb
    • Categories Constrained Nonlinear Optimization, Nonsmooth Optimization Tags , , , ,

    We propose an expansion of the scope of the alternating direction method of multipliers (ADMM). Specifically, we show that ADMM, when employed to solve problems with multiaffine constraints that satisfy certain easily verifiable assumptions, converges to the set of constrained stationary points if the penalty parameter in the augmented Lagrangian is sufficiently large. When the … Read more

    Block BFGS Methods

  • Wenbo Gao
  • Donald Goldfarb
    • Categories Unconstrained Optimization Tags , , ,

    We introduce a quasi-Newton method with block updates called Block BFGS. We show that this method, performed with inexact Armijo-Wolfe line searches, converges globally and superlinearly under the same convexity assumptions as BFGS. We also show that Block BFGS is globally convergent to a stationary point when applied to non-convex functions with bounded Hessian, and … Read more