Conjugate gradient method for the linear complementarity problem with S-matrix

Authors:
Dong-Hui Li;Yi-Yong Nie;Jin-Ping Zeng;Qing-Na Li
Affiliations:
Shenyang Institute of Automation, Chinese Academy of Sciences, China and College of Mathematics and Econometrics, Hunan University, Changsha, 410082, China;Shenyang Institute of Automation, Chinese Academy of Sciences, China;College of Mathematics and Econometrics, Hunan University, Changsha, 410082, China and College of Software, Dongguan University of Technology, China;College of Mathematics and Econometrics, Hunan University, Changsha, 410082, China
Venue:
Mathematical and Computer Modelling: An International Journal
Year:
2008

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Abstract

In this paper, we present a conjugate gradient method for solving the linear complementarity problem that involves an S-matrix. At each step, we solve a lower-dimensional system of linear equations by conjugate gradient method. The method terminates at the exact solution of the problem after a finite number of iterations. Moreover, the computational complexity of the proposed method is no more than the computational complexity of a conjugate gradient method for solving a system of linear equations. Preliminary numerical experiments show that the method is efficient.