Article ID: | iaor20022501 |
Country: | Netherlands |
Volume: | 103 |
Issue: | 1 |
Start Page Number: | 71 |
End Page Number: | 97 |
Publication Date: | Mar 2001 |
Journal: | Annals of Operations Research |
Authors: | Fukushima Masao, Li Dong-Hui |
In this paper, we propose a general smoothing Broyden-like quasi-Newton method for solving a class of nonsmooth equations. Under appropriate conditions, the proposed method converges to a solution of the equation globally and superlinearly. In particular, the proposed method provides the possibility of developing a quasi-Newton method that enjoys superlinear convergence even if strict complementarity fails to hold. We pay particular attention to semismooth equations arising from nonlinear complementarity problems, mixed complementarity problems and variational inequality problems. We show that under certain conditions, the related methods based on the perturbed Fischer–Burmeister function, Chen–Harker–Kanzow–Smale smoothing function and the Gabriel–Moré class of smoothing functions converge globally and superlinearly.