Quasi-newton methods for monlinear equations and unconstrained optimization problems

Abstract

In the first part of this paper we present a method for solving nonlinear equations. The convergence results are direct generalizations of the results of Broyden, Dennis and Moré [2] and Dennis and Walker [4]. In the second part we present an algorithm for solving unconstrained optimization problems. We prove that this algorithm converges and the rate of convergence is superlinear.

Keywords:

• Quasi-Newton methods
• nonlinear equations
• unconstrained optimization