The Stability and Convergence Analysis of a New Conjugate Gradient Method for Solving Nonlinear Optimization Problems

Abstract

The development of any conjugate gradient method could be viewed from the perspective of approximating an objective function ) (x f by a functional ) (x F noting that the properties of the functional can be used to characterize the method. Using the functional ) (x F , the new conjugate gradient method was developed and used to solve many nonlinear optimization problems with high efficiency and accuracy. The numeric analysis of its stability and convergence becomes imperative in order to establish the reliability of the method and satisfy the yearnings of its increasing users. In this paper, we present the stability and convergence analysis of the new conjugate gradient method.