Global convergence of a filter-trust-region algorithm for solving nonsmooth equations

Abstract

In this paper, we present a new algorithm for solving nonsmooth equations, where the function is locally Lipschitzian. The algorithm attempts to combine the efficiency of filter techniques and the robustness of trust-region method. Global convergence for this algorithm is established under reasonable assumptions.

Keywords:

• nonsmooth equations
• trust-region algorithm
• filter technique
• global convergence

2000 AMS Subject Classification :

• 65K05
• 90C30
• 90C33

Acknowledgements

The authors would like to thank two anonymous referees for their valuable suggestions and comments that improve the quality of this manuscript. This work was supported by the Research Grant Council of Hong Kong, the National Natural Science Foundation of China Nos 10231060 and 10501024, the Specialized Research Fund of Doctoral Program of Higher Education of China at No. 20040319003, and the Natural Science Fund of Jiangsu Province of China at Grant No. BK2006214.