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Globalizing a nonsmooth Newton method via nonmonotone path search


Bütikofer, Stephan (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.

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.

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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
Scopus Subject Areas:Physical Sciences > Software
Physical Sciences > General Mathematics
Social Sciences & Humanities > Management Science and Operations Research
Language:English
Date:2008
Deposited On:28 Aug 2019 15:12
Last Modified:16 Apr 2020 00:07
Publisher:Springer
ISSN:1432-2994
Additional Information:The original publication is available at www.springerlink.com
OA Status:Green
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
Other Identification Number:merlin-id:1111

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