Bulletin of the Australian Mathematical Society

Research Article

A MULTIPLICATIVE SCHWARZ ALGORITHM FOR THE NONLINEAR COMPLEMENTARITY PROBLEM WITH AN M-FUNCTION

YINGJUN JIANGa1 and JINPING ZENGa2 c1

a1 Department of Mathematics and Science Computing, Changsha University of Science and Technology, Changsha, 410004, PR China (email: [email protected])

a2 College of Computer Science, Dongguan University of Technology, Dongguan, 523005, PR China (email: [email protected])

Abstract

A multiplicative Schwarz iteration algorithm is presented for solving the finite-dimensional nonlinear complementarity problem with an M-function. The monotone convergence of the iteration algorithm is obtained with special choices of initial values. Moreover, by applying the concept of weak regular splitting, the weighted max-norm bound is derived for the iteration errors.

(Received June 16 2008)

2000 Mathematics subject classification

  • primary 90C33

Keywords and phrases

  • multiplicative Schwarz algorithm;
  • M-function;
  • nonlinear complementarity problem;
  • monotone convergence;
  • weighted max-norm

Footnotes

This work is supported by the National Natural Science Foundation of China (Grants 10901027, 10971058).