Department of Applied Mathematics & Physics, Kyoto Univiversity
Technical Report #99004 (March, 1999)
A Derivative-Free Line Search and Global Convergence of Broyden-Like Method for Nonlinear Equations
by Dong-Hui Li and Masao Fukushima
In this paper, by using derivative-free line search, we propose
quasi-Newton methods for smooth nonlinear equations.
Under appropriate conditions, we show that the proposed quasi-Newton methods
converge globally and superlinearly.
In particular, for nonlinear equations involving a mapping with
positive definite Jacobian matrices, we propose a
norm descent quasi-Newton method and establish its global and