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 superlinear convergence.