Uniform Convergence of the Newton Method for Aubin Continuous Maps

@article{Dontchev1996,
abstract = {* This work was supported by National Science Foundation grant DMS 9404431.In this paper we prove that the Newton method applied to the generalized equation y ∈ f(x) + F(x) with a C^1 function f and a set-valued map F acting in Banach spaces, is locally convergent uniformly in the parameter y if and only if the map (f +F)^(−1) is Aubin continuous at the reference point. We also show that the Aubin continuity actually implies uniform Q-quadratic convergence provided that the derivative of f is Lipschitz continuous. As an application, we give a characterization of the uniform local Q-quadratic convergence of the sequential quadratic programming method applied to a perturbed nonlinear program.},
author = {Dontchev, Asen},
journal = {Serdica Mathematical Journal},
keywords = {Generalized Equation; Newton’s Method; Sequential Quadratic Programming; Aubin continuity; sequential quadratic programming; perturbed nonlinear program},
language = {eng},
number = {3},
pages = {385-398},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {Uniform Convergence of the Newton Method for Aubin Continuous Maps},
url = {http://eudml.org/doc/11643},
volume = {22},
year = {1996},
}

TY - JOUR
AU - Dontchev, Asen
TI - Uniform Convergence of the Newton Method for Aubin Continuous Maps
JO - Serdica Mathematical Journal
PY - 1996
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 22
IS - 3
SP - 385
EP - 398
AB - * This work was supported by National Science Foundation grant DMS 9404431.In this paper we prove that the Newton method applied to the generalized equation y ∈ f(x) + F(x) with a C^1 function f and a set-valued map F acting in Banach spaces, is locally convergent uniformly in the parameter y if and only if the map (f +F)^(−1) is Aubin continuous at the reference point. We also show that the Aubin continuity actually implies uniform Q-quadratic convergence provided that the derivative of f is Lipschitz continuous. As an application, we give a characterization of the uniform local Q-quadratic convergence of the sequential quadratic programming method applied to a perturbed nonlinear program.
LA - eng
KW - Generalized Equation; Newton’s Method; Sequential Quadratic Programming; Aubin continuity; sequential quadratic programming; perturbed nonlinear program
UR - http://eudml.org/doc/11643
ER -