Department of Applied Mathematics & Physics, Kyoto Univiversity

Technical Report #99007 (April, 1999)

On the Global Convergence of BFGS Method for Nonconvex Unconstrained Optimization Problems
by Dong-Hui Li and Masao Fukushima

This paper is concerned with the open problem whether BFGS method with inexact line search converges globally when applied to nonconvex unconstrained optimization problems. We propose a cautious BFGS update and prove that the method with either Wolfe-type or Armijo-type line search converges globally if the function to be minimized has Lipschitz continuous gradients.