Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Serdica Mathematical Journal, Vol. 22, No 3, (1996), 385p-398p
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.
* This work was supported by National Science Foundation grant DMS 9404431.