Abstract
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–More class of smoothing functions converge globally and superlinearly.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
