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Globalizing a nonsmooth Newton method via nonmonotone path search


Bütikofer, S (2008). Globalizing a nonsmooth Newton method via nonmonotone path search. Mathematical Methods of Operations Research, 68(2):235-256.

Abstract

We give a framework for the globalization of a nonsmooth Newton method. In part one we start with recalling B. Kummer's approach to convergence analysis of a nonsmooth Newton method and state his results for local convergence. In part two we give a globalized version of this method.
Our approach uses a path search idea to control the descent. After elaborating the single steps, we analyze and prove the global convergence resp. the local superlinear or quadratic convergence of the algorithm. In the third part we illustrate the method for nonlinear complementarity problems.

We give a framework for the globalization of a nonsmooth Newton method. In part one we start with recalling B. Kummer's approach to convergence analysis of a nonsmooth Newton method and state his results for local convergence. In part two we give a globalized version of this method.
Our approach uses a path search idea to control the descent. After elaborating the single steps, we analyze and prove the global convergence resp. the local superlinear or quadratic convergence of the algorithm. In the third part we illustrate the method for nonlinear complementarity problems.

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1 citation in Web of Science®
2 citations in Scopus®
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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:03 Faculty of Economics > Department of Business Administration
Dewey Decimal Classification:330 Economics
Language:English
Date:2008
Deposited On:26 Feb 2009 08:27
Last Modified:05 Apr 2016 13:06
Publisher:Springer
ISSN:1432-2994
Additional Information:The original publication is available at www.springerlink.com
Publisher DOI:https://doi.org/10.1007/s00186-008-0219-8
Official URL:http://search.ebscohost.com/login.aspx?direct=true&db=buh&AN=34529470&loginpage=Login.asp&site=ehost-live
Permanent URL: https://doi.org/10.5167/uzh-16441

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