A smoothing inexact Newton method for variational inequality problems

Abstract

In this paper, we reformulate the variational inequality problem as an equivalent smooth non-linear equation system by introducing the Chen–Harker–Kanzow–Smale smoothing function. A new smoothing inexact Newton algorithm is proposed to solve the smooth equations. In each iteration, the corresponding linear system is solved approximately. We prove that the proposed algorithm converges globally and superlinearly under mild conditions. Preliminary numerical results indicate that the method is effective.

Keywords:

• variational inequality problem
• smoothing method
• inexact Newton algorithm
• global convergence
• superlinear convergence

2010 AMS Subject Classification :

• 90C33

Acknowledgements

This author's work was supported by the Fundamental Research Funds for the Central Universities (No. JY10000970004).