On the solution and applications of generalized equations using Newton's method

Ioannis K. Argyros. "On the solution and applications of generalized equations using Newton's method." Applicationes Mathematicae 31.2 (2004): 229-242. <http://eudml.org/doc/279284>.

@article{IoannisK2004,
abstract = {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.},
author = {Ioannis K. Argyros},
journal = {Applicationes Mathematicae},
keywords = {Hilbert space; Newton's method; local convergence; local and semilocal convergence; multivalued maximal monotone operator; radius of convergence; nonlinear operator equation; Lipschitz conditions; numerical examples},
language = {eng},
number = {2},
pages = {229-242},
title = {On the solution and applications of generalized equations using Newton's method},
url = {http://eudml.org/doc/279284},
volume = {31},
year = {2004},
}

TY - JOUR
AU - Ioannis K. Argyros
TI - On the solution and applications of generalized equations using Newton's method
JO - Applicationes Mathematicae
PY - 2004
VL - 31
IS - 2
SP - 229
EP - 242
AB - 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.
LA - eng
KW - Hilbert space; Newton's method; local convergence; local and semilocal convergence; multivalued maximal monotone operator; radius of convergence; nonlinear operator equation; Lipschitz conditions; numerical examples
UR - http://eudml.org/doc/279284
ER -