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A. Dontchev, V.M. Veliov:
"Metric regularity under approximations";
Control and Cybernetics (invited), 39 (2009), 4.

In this paper we show that metric regularity and
strong metric regularity of a set-valued mapping imply convergence
of inexact iterative methods for solving a generalized equation associated with this mapping. To accomplish this, we first focus on the question how these properties are preserved under changes of the
mapping and the reference point. As an application, we consider
discrete approximations in optimal control.

metric regularity, inexact iterative methods, Newton method, proximal point method, discrete approximation, optimal control