Copyright © 2012 Zhong Jin and Yuqing Wang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

An improved line search filter algorithm for the system of nonlinear equations is presented. We divide the equations into two groups, one contains the equations that are treated as equality constraints and the square of other equations is regarded as objective function. Two groups of equations are updated at every iteration in the works by Nie (2004, 2006, and 2006), by Nie et al. (2008), and by Gu (2011), while we just update them at the iterations when it is needed indeed. As a consequence, the scale of the calculation is decreased in a certain degree. Under some suitable conditions the global convergence can be induced. In the end, numerical experiments show that the method in this paper is effective.