We provide local and semilocal convergence results for Newton's method when used to solve generalized equations. Using Lipschitz as well as center-Lipschitz conditions on the operators involved instead of just Lipschitz conditions we show that our Newton-Kantorovich hypotheses are weaker than earlier sufficient conditions for the convergence of Newton's method. In the semilocal case we provide finer error bounds and a better information on the location of the solution. In the local case we can provide a larger convergence radius. Our results apply to generalized equations involving single as well as multivalued operators, which include variational inequalities, nonlinear complementarity problems and nonsmooth convex minimization problems.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-am31-2-7,
author = {Ioannis K. Argyros},
title = {On the solution and applications of generalized equations using Newton's method},
journal = {Applicationes Mathematicae},
volume = {31},
year = {2004},
pages = {229-242},
zbl = {1057.65030},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am31-2-7}
}
Ioannis K. Argyros. On the solution and applications of generalized equations using Newton's method. Applicationes Mathematicae, Tome 31 (2004) pp. 229-242. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am31-2-7/