The relaxation modulus-based matrix splitting iteration method for solving a class of nonlinear complementarity problems

ABSTRACT

In this paper, by the relaxation technique, the relaxation modulus-based matrix splitting iteration method is presented for solving a class of nonlinear complementarity problems. The convergence conditions are given when the system matrix is a positive definite matrix or an H-matrix. The strategy of the choice of the relaxation parameters is discussed. Numerical examples show that the proposed method is efficient and accelerates the convergence performance of the modulus-based matrix splitting iteration method and the projection-based matrix splitting iteration method.

KEYWORDS:

• Nonlinear complementarity problem
• relaxation
• modulus-based matrix splitting iteration method
• H-matrix
• positive definite matrix

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 65F10
• 90C33

Acknowledgments

The authors would like to thank the referees for their helpful comments.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Hua Zheng  http://orcid.org/0000-0002-2822-0078

Additional information

Funding

The work was supported by the National Natural Science Foundation of China [grant number 11601340], University of Macau [grant number MYRG2017-00098-FST], Macao Science and Technology Development Fund [grant number 050/2017/A], the Opening Project of Guangdong Provincial Engineering Technology Research Center for Data Sciences [grant number 2016KF11] and Science and Technology Planning Project of Shaoguan [grant number SHAOKE [2016]44/15].