A globally and locally superlinearly convergent inexact Newton-GMRES method for large-scale variational inequality problem

Abstract

In this paper, we propose an inexact Newton-generalized minimal residual method for solving the variational inequality problem. Based on a new smoothing function, the variational inequality problem is reformulated as a system of parameterized smooth equations. In each iteration, the corresponding linear system is solved only approximately. Under mild assumptions, it is proved that the proposed algorithm has global convergence and local superlinear convergence properties. Preliminary numerical results indicate that the method is effective for a large-scale variational inequality problem.

Keywords:

• variational inequality problem
• inexact Newton-GMRES method
• large-scale problems
• global convergence
• superlinear convergence

2000 AMS Subject Classification:

• 90C33

Acknowledgements

The authors thank the referees for valuable comments. This research was supported by the Anhui Province Education Department, Natural Science Research Item (No: KJ2013A235).