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.