Modulus-based matrix splitting iteration methods with new splitting scheme for horizontal implicit complementarity problems

Abstract

In this paper, we propose the horizontal implicit complementarity problems, which cover many complementarity problems that have wide applications. After reformulating the horizontal implicit complementarity problem as an implicit fixed-point equation, the modulus-based matrix splitting iteration methods are applied to solve the problems. Besides, this paper introduces a new kind of matrix splitting, called modulus-based Hermitian and skew-Hermitian matrix relaxation splitting. The corresponding modulus-based matrix splitting iteration method is shown superior to the nonsmooth Newton's method and the existing matrix splitting schemes by some numerical experiments. The convergence analysis is given and validates that our methods are more practical in applications.

Keywords:

• Horizontal implicit complementarity problems
• modulus-based matrix splitting iteration methods
• Hermitian and Skew-Hermitian
• relaxation splitting

Acknowledgments

The authors would like to thank the reviewers for their helpful comments, which improved the paper greatly.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work is funded by the Science and Technology Development Fund, Macau SAR (File no. 0005/2019/A), University of Macau (File no. MYRG2020-00035-FST, MYRG2018-00047-FST), Major Projects of Guangdong Education Department for Foundation Research and Applied Research [grant number 2018KZDXM065], Scientific Computing Research Innovation Team of Guangdong Province [grant number 2021KCXTD052], Technology Planning Project of Shaoguan [grant number 210716094530390] and Science Foundation of Shaoguan University [grant number SZ2020KJ01].