Error bounds for the solution sets of generalized polynomial complementarity problems

ABSTRACT

In this paper, several error bounds for the solution sets of the generalized polynomial complementarity problems (GPCPs) with explicit exponents are given. As the solution set of a GPCP is the solution set of a system of polynomial equalities and inequalities, the state-of-art results in error bounds for polynomial systems can be applied directly. Starting from this, a much better error bound result for the solution set of a GPCP based on exploring the intrinsic sparsity via tensor decomposition is established.

Keywords:

• Generalized polynomial complementarity problem
• error bound
• tensor decomposition

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 90C33
• 65L70
• 13P15

Acknowledgements

This work is partially supported by National Natural Science Foundation of China (Grant No. 11901549). The author is very grateful for the annoynous referees for their helpful suggestions and comments in revising this paper.

Disclosure statement

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

Additional information

Funding

This work is partially supported by National Natural Science Foundation of China [grant number 11901549].