A two-step new modulus-based matrix splitting method for vertical linear complementarity problem

Abstract

In this paper, for solving the vertical linear complementarity problem (VLCP) effectively, a two-step new modulus-based matrix splitting (TNMMS) iteration method is introduced. Its convergence properties are discussed in depth. The efficiency of the proposed method is confirmed by some numerical experiments from the 2-D boundary problem. Numerical results show that the proposed method is superior to some existing methods, such as the two modulus-based matrix splitting (TMMS) iteration method (Numer. Algor., 2011, 57: 83–99) and the new modulus-based matrix splitting (NMMS) iteration method (Optim., 2023, 72: 2499–2516).

Keywords:

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

AMS Subject Classifications:

• 90C33
• 65F10
• 65F50
• 65G40

Acknowledgments

The authors would like to thank associate editor and 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 [grant number 11961082].

Notes on contributors

Cuixia Li

Cuixia Li, work at Yunnan Normal University. Prof. Li is interested in numerical linear algebra, including complementarity problem, absolute value equation and so on.

Shiliang Wu

Shiliang Wu, work at Yunnan Normal University. Prof. Wu at present focus on numerical linear algebra and optimization.