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On properties of Newton's method for smooth and nonsmooth equations
Parallel Algorithms Group, CERFACS, Toulouse, France.ORCID iD: 0000-0003-1836-4200
1995 (English)In: Recent Trends in Optimization Theory and Applications / [ed] R.P. Agarwal, World Scientific, 1995, 17-24 p.Chapter in book (Other academic)
Abstract [en]

Variational inequalities, nonlinear programming, complementarity problems and other problems can be reduced to nonsmooth equations, for which some generalizations of Newton's method are known. The Newton path, as a natural generalization of the Newton direction, was suggested by D.Ralph for enlarging the convergence region (globalization) of Newton-Robinson's method in the nonsmooth case. We investigate some properties of both the Newton direction and the Newton path, which seem to be basic for various globalization strategies. In particular, a simple formula for the derivative of an arbitrary norm of residuals along the Newton direction,derived earlier by the author for the smooth equations, is generalizedhere for the derivative along the Newton path.

Place, publisher, year, edition, pages
World Scientific, 1995. 17-24 p.
Series
World Scientific series in applicable analysis, 5
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-78986ISBN: 978-981-02-2382-3 (print)ISBN: 978-981-279-886-2 (print)OAI: oai:DiVA.org:liu-78986DiVA: diva2:537460
Available from: 2012-06-26 Created: 2012-06-26 Last updated: 2015-06-02

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Burdakov, Oleg

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  • nn-NB
  • sv-SE
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