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Title: Uniform Convergence of the Newton Method for Aubin Continuous Maps
Authors: Dontchev, Asen
Keywords: Generalized Equation
Newton’s Method
Sequential Quadratic Programming
Issue Date: 1996
Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation: Serdica Mathematical Journal, Vol. 22, No 3, (1996), 385p-398p
Abstract: 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.
Description: * This work was supported by National Science Foundation grant DMS 9404431.
ISSN: 1310-6600
Appears in Collections:Volume 22 Number 3

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