A class of modulus-based matrix splitting methods for vertical linear complementarity problem

Abstract

In this paper, by transforming the vertical linear complementarity problem (VLCP) as a certain absolute value equation, we design a class of modulus-based matrix splitting iteration methods for solving the VLCP. The convergence properties of the proposed methods are discussed in depth. By making use of some numerical experiments, we confirm the efficiency of the proposed methods. Numerical results show that the proposed methods are superior to the classical modulus-based matrix splitting iteration methods.

Keywords:

• Vertical linear complementarity problem
• modulus-based matrix splitting
• iteration method
• convergence

AMS classifications:

• 90C33
• 65F10
• 65F50
• 65G40

Acknowledgments

The authors would like to thank two anonymous referees for providing helpful suggestions, which greatly improved the paper.

Disclosure statement

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

Additional information

Funding

This research was supported by the National Natural Science Foundation of China [No.11961082].