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Mathematical Problems in Engineering
Volume 2012, Article ID 971468, 15 pages
Research Article

A Nonmonotone Line Search Filter Algorithm 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 9 June 2012; Accepted 23 June 2012

Academic Editor: Wei-Chiang Hong

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.


We present a new iterative method based on the line search filter method with the nonmonotone strategy to solve the system of nonlinear equations. The equations are divided into two groups; some equations are treated as constraints and the others act as the objective function, and the two groups are just updated at the iterations where it is needed indeed. We employ the nonmonotone idea to the sufficient reduction conditions and filter technique which leads to a flexibility and acceptance behavior comparable to monotone methods. The new algorithm is shown to be globally convergent and numerical experiments demonstrate its effectiveness.