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Metric regularity under approximations

Dontchev A. L., Veliov V. M.

Control and Cybernetics

2009

Vol. 38, no 4B

1283-1303

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.