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Journal of Global Optimization

, Volume 52, Issue 4, pp 843–853 | Cite as

Stability properties of the Tikhonov regularization for nonmonotone inclusions

  • Michaël Gaydu
Article

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.

Keywords

Tikhonov regularization Set-valued mapping Metric regularity Strong regularity 

Mathematics Subject Classification (2000)

49J53 49J40 90C48 

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Copyright information

© Springer Science+Business Media, LLC. 2011

Authors and Affiliations

  1. 1.LAMIA, Dpt. de MathématiquesUniversité Antilles-GuyanePointe-à-Pitre, GuadeloupeFrance

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