• Original Articles •

### A SMOOTHING TRUST REGION METHOD FOR NCPS BASED ON THE SMOOTHING GENERALIZED FISCHER-BURMEISTER FUNCTION

Xuebin Wang, Changfeng Ma, Meiyan Li

1. School of Mathematics and Computer Science, Fujian Normal University, Fuzhou 350007, China; School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin 541004, China
• Received:2009-09-27 Revised:2010-03-22 Online:2011-05-15 Published:2011-05-15
• Supported by:

The work was supported by the National Natural Science Foundation of China (11071041) and Fujian Natural Science Foundation (2009J01002).

Xuebin Wang, Changfeng Ma, Meiyan Li. A SMOOTHING TRUST REGION METHOD FOR NCPS BASED ON THE SMOOTHING GENERALIZED FISCHER-BURMEISTER FUNCTION[J]. Journal of Computational Mathematics, 2011, 29(3): 261-286.

Based on a reformulation of the complementarity problem as a system of nonsmooth equations by using the generalized Fischer-Burmeister function, a smoothing trust region algorithm with line search is proposed for solving general (not necessarily monotone) nonlinear complementarity problems. Global convergence and, under a nonsingularity assumption, local Q-superlinear/Q-quadratic convergence of the algorithm are established. In particular, it is proved that a unit step size is always accepted after a finite number of iterations. Numerical results also confirm the good theoretical properties of our approach.

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