Please use this identifier to cite or link to this item: http://hdl.handle.net/10525/613

 Title: Uniform Convergence of the Newton Method for Aubin Continuous Maps Authors: Dontchev, Asen Keywords: Generalized EquationNewton’s MethodSequential 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. URI: http://hdl.handle.net/10525/613 ISSN: 1310-6600 Appears in Collections: Volume 22 Number 3

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