On the splitting iteration method for Pareto eigenvalue complementarity problems of H₊-matrices

Abstract

We present a class of inexact splitting-modulus iteration methods for solving the Pareto Eigenvalue Complementarity Problem (EiCP) when the system matrix A is an $H_{+}$-matrix. Our method first employs the matrix splitting technique to transform the original eigenvalue complementarity problem (EiCP) into an easily solvable Linear Complementarity Problem (LCP), and the inner iterative process corresponds to the inexact split iterative process when the modulus iteration method is used, where we employed an effective and fast inner iterative stopping criterion. We then provide a convergence proof for inexact matrix splitting iteration methods. Numerical experiments demonstrate that our proposed algorithms exhibit significant superiority over the classical matrix splitting iteration method in terms of computational time, especially for solving large-scale symmetric and asymmetric eigenvalue complementarity problems of $H_{+}$-matrices.

Keywords:

• Eigenvalue complementarity problem
• matrix splitting
• modulus iteration method
• H₊-matrix

2020 Mathematics Subject Classifications:

• 65F10
• 65F15
• 65K10
• 90C33

Acknowledgments

The authors would like to express their sincere appreciation to the anonymous reviewers for their valuable comments that greatly improved the presentation of the manuscript.

Disclosure statement

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

Additional information

Funding

The work is supported by the National Natural Science Foundation of China (Grant Numbers 11871205).