Journal of Applied Mathematics
Volume 2012 (2012), Article ID 273141, 15 pages
Research Article

An Improved Line Search Filter Method for the System of Nonlinear Equations

1Department of Mathematics, Shanghai Maritime University, Shanghai 201306, China
2Xianda College of Economics and Humanities, Shanghai International Studies University, Shanghai 200083, China

Received 20 March 2012; Accepted 17 September 2012

Academic Editor: Hak-Keung Lam

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.


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.