# Uniform Convergence of the Newton Method for Aubin Continuous Maps

Serdica Mathematical Journal (1996)

- Volume: 22, Issue: 3, page 385-398
- ISSN: 1310-6600

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topDontchev, Asen. "Uniform Convergence of the Newton Method for Aubin Continuous Maps." Serdica Mathematical Journal 22.3 (1996): 385-398. <http://eudml.org/doc/11643>.

@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 -

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