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Journal of Applied Mathematics
Volume 2013, Article ID 671402, 6 pages
Research Article

A Superlinearly Convergent Method for the Generalized Complementarity Problem over a Polyhedral Cone

1School of Management Science, Qufu Normal University, Rizhao, Shandong 276800, China
2Software Center, Northeastern University, Shenyang, Liaoning 110004, China
3College of Information Science and Engineering, Northeastern University, Shenyang, Liaoning 110004, China

Received 24 April 2013; Accepted 22 July 2013

Academic Editor: Turgut Öziş

Copyright © 2013 Fengming Ma et al. 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.


Making use of a smoothing NCP-function, we formulate the generalized complementarity problem (GCP) over a polyhedral cone as an equivalent system of equations. Then we present a Newton-type method for the equivalent system to obtain a solution of the GCP. Our method solves only one linear system of equations and performs only one line search at each iteration. Under mild assumptions, we show that our method is both globally and superlinearly convergent. Compared to the previous literatures, our method has stronger convergence results under weaker conditions.