A new homotopy method for solving non-linear complementarity problems

Abstract

In this article, a new homotopy method is proposed for solving the non-linear complementarity problem. An existence condition for a finite homotopy path is derived from the limiting behaviours of the complementarity mapping at infinity. This condition is different from any existing ones in the literature and can be easily verified. The method guarantees the existence of a solution to the non-linear complementarity problem without the mapping being P ₀ or monotone. Numerical results show that the method is effective and efficient.

Keywords:

• non-linear complementarity
• homotopy
• path-following
• continuation method
• global convergence

Mathematics Subject Classifications 2000:

• 90C33
• 65K05

Acknowledgements

This research was partially supported by the National Natural Science Foundation of China (70432001) the Research Fund of Shanghai (07JC14001) and CERG: CityU 101003 of the Government of Hong Kong SAR.