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

Dong Hui Li; Yi Yong Nie; Jin Ping Zeng; Qing Na Li

doi:10.1016/j.mcm.2007.10.017

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

Dong Hui Li^*, Yi Yong Nie, Jin Ping Zeng, Qing Na Li

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

10 Citations (Scopus)

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.

Original language	English
Pages (from-to)	918-928
Number of pages	11
Journal	Mathematical and Computer Modelling
Volume	48
Issue number	5-6
DOIs	https://doi.org/10.1016/j.mcm.2007.10.017
Publication status	Published - Sept 2008
Externally published	Yes

Keywords

Conjugate gradient method
Linear complementarity problem
S-matrix

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10.1016/j.mcm.2007.10.017

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Li, D. H., Nie, Y. Y., Zeng, J. P., & Li, Q. N. (2008). Conjugate gradient method for the linear complementarity problem with S-matrix. Mathematical and Computer Modelling, 48(5-6), 918-928. https://doi.org/10.1016/j.mcm.2007.10.017

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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.",

keywords = "Conjugate gradient method, Linear complementarity problem, S-matrix",

author = "Li, {Dong Hui} and Nie, {Yi Yong} and Zeng, {Jin Ping} and Li, {Qing Na}",

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AU - Li, Dong Hui

AU - Nie, Yi Yong

AU - Zeng, Jin Ping

AU - Li, Qing Na

PY - 2008/9

Y1 - 2008/9

N2 - 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.

AB - 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.

KW - Conjugate gradient method

KW - Linear complementarity problem

KW - S-matrix

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EP - 928

JO - Mathematical and Computer Modelling

JF - Mathematical and Computer Modelling

IS - 5-6

ER -

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

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Keywords

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