Geodesic
Uniform Convergence of the Newton Method for Aubin Continuous Maps
Serdica Mathematical Journal, Tome 22 (1996) no. 3, pp. 385-398.

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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.
Keywords: Generalized Equation, Newton’s Method, Sequential Quadratic Programming 
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     author = {Dontchev, Asen},
     title = {Uniform {Convergence} of the {Newton} {Method} for {Aubin} {Continuous} {Maps}},
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Dontchev, Asen. Uniform Convergence of the Newton Method for Aubin Continuous Maps. Serdica Mathematical Journal, Tome 22 (1996) no. 3, pp. 385-398. http://geodesic.mathdoc.fr/item/SMJ2_1996_22_3_a6/