Abstract
We study the Tikhonov regularization for perturbed inclusions of the form \({T(x) \ni y^*}\) where T is a set-valued mapping defined on a Banach space that enjoys metric regularity properties and y* is an element near 0. We investigate the case when T is metrically regular and strongly regular and we show the existence of both a solution x* to the perturbed inclusion and a Tikhonov sequence which converges to x*. Finally, we show that the Tikhonov sequences associated to the perturbed problem inherit the regularity properties of the inverse of T.
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This author is supported by Contract EA4540 (France).
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Gaydu, M. Stability properties of the Tikhonov regularization for nonmonotone inclusions. J Glob Optim 52, 843–853 (2012). https://doi.org/10.1007/s10898-011-9715-0
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DOI: https://doi.org/10.1007/s10898-011-9715-0