## Bulletin of the Belgian Mathematical Society - Simon Stevin

### One-step smoothing inexact Newton method for nonlinear complementarity problem with a $P_0$ function

#### Abstract

Based on Fischer-Burmeister function, we propose a new smoothing function. Using this function,the existence and continuity of the smooth path for solving the nonlinear complementarity problem with a $P_0$ function are discussed. Then we present a one-step smoothing inexact Newton method for nonlinear complementarity problem with a $P_0$ function. The proposed method solves the corresponding linear system approximately in each iteration. Furthermore, we investigate the boundedness of the sequence generated by our algorithm and prove the global convergence and local superlinear convergence under mild conditions.

#### Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 19, Number 2 (2012), 277-287.

Dates
First available in Project Euclid: 24 May 2012

https://projecteuclid.org/euclid.bbms/1337864272

Digital Object Identifier
doi:10.36045/bbms/1337864272

Mathematical Reviews number (MathSciNet)
MR2977231

Zentralblatt MATH identifier
1242.90266

#### Citation

Wu, Caiying; Zhao, Yue. One-step smoothing inexact Newton method for nonlinear complementarity problem with a $P_0$ function. Bull. Belg. Math. Soc. Simon Stevin 19 (2012), no. 2, 277--287. doi:10.36045/bbms/1337864272. https://projecteuclid.org/euclid.bbms/1337864272