THE PROPERTIES OF A NEW SMOOTHING FUNCTION AND A REGULARIZED SMOOTHING NEWTON METHOD FOR THE P0-NCP
LI DONG *
College of Mathematics and Information Science, Xinyang Normal University, Xinyang 464000, China.
RUIJUAN LIU
Department of Mathematics and Physics, Nanjing Institute of Technology, Nanjing 210028, China.
*Author to whom correspondence should be addressed.
Abstract
In this paper we introduce a new smoothing function by smoothing the Fischer-Burmeister function. This function has coerciveness under suitable conditions which plays an important role in the convergence analysis of smoothing-type methods. Based on this new function, we propose a regularized smoothing Newton method for solving the nonlinear complementarity problem with P0-function. It is proved that the proposed method is globally and locally quadratically convergent in absence of strict complementarity condition at the optimal solution. Some numerical results are reported which indicate the effectiveness of our method.
Keywords: Nonlinear complementarity problem, P0-function, smoothing Newton method, global convergence, quadratic convergence