Title: Newton and Quasi-Newton Methods for a Class of Nonsmooth Equations and Related Problems
Abstract: The paper presents concrete realizations of quasi-Newton methods for solving several standard problems including complementarity problems, special variational inequality problems, and the Karush--Kuhn--Tucker (KKT) system of nonlinear programming. A new approximation idea is introduced in this paper. The Q-superlinear convergence of the Newton method and the quasi-Newton method are established under suitable assumptions, in which the existence of F'(x*) is not assumed. The new algorithms only need to solve a linear equation in each step. For complementarity problems, the QR factorization on the quasi-Newton method is discussed.
Publication Year: 1997
Publication Date: 1997-05-01
Language: en
Type: article
Indexed In: ['crossref']
Access and Citation
Cited By Count: 93
AI Researcher Chatbot
Get quick answers to your questions about the article from our AI researcher chatbot