A Superlinearly Convergent Method for the Generalized Complementarity Problem over a Polyhedral Cone. (25th August 2013)

• Record Type: Journal Article
• Authors: Ma, Fengming; Sheng, Gang; Yin, Ying
• Other Names: Öziş Turgut Academic Editor.
• Is Part Of: Journal of applied mathematics. Volume 2013(2013)
• Publication Date: 2013-08-25
• Subjects: Mathematics -- Periodicals; 519.05
• DOI: 10.1155/2013/671402
• Languages: English
• ISSNs: 1110-757X

Abstract

Abstract : 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.