×

Newton methods for solving nonsmooth equations via a new subdifferential. (English) Zbl 1031.90069

Summary: A new subdifferential for a locally Lipschitzian function is proposed. Based on this subdifferential, Newton methods and inexact-Newton methods for solving the system of nonsmooth equations and for solving the system of equations of smooth compositions of nonsmooth functions, are developed. The \(Q\)-superlinear convergence of Newton methods and the \(Q\)-linear convergence of inexact-Newton methods are shown. The present Newton methods and inexact-Newton methods could be viewed as the extensions of previous ones with same convergent results.

MSC:

90C53 Methods of quasi-Newton type
49J52 Nonsmooth analysis
65H10 Numerical computation of solutions to systems of equations
PDF BibTeX XML Cite
Full Text: DOI