Tikhonov regularization of metrically regular inclusions

Tikhonov regularization of metrically regular inclusions We present a Tikhonov regularization method for inclusions of the form $$T(x) \ni 0$$ where T is a set-valued mapping defined on a Banach space that enjoys metric regularity properties. We investigate, subsequently, the case when the mapping T is metrically regular, strongly metrically regular, strongly subregular and Lipschitz continuous and show the strong convergence of the solutions of regularized problems to a solution to the original inclusion $$T(x) \ni 0$$ . We also prove that the method has finite termination under some special conditioning assumptions on T and we study its stability with respect to some variational perturbations. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

Tikhonov regularization of metrically regular inclusions

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Publisher
Birkhäuser-Verlag
Copyright
Copyright © 2008 by Birkhäuser Verlag Basel/Switzerland
Subject
Mathematics; Fourier Analysis; Operator Theory; Potential Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1007/s11117-008-2228-5
Publisher site
See Article on Publisher Site

Abstract

We present a Tikhonov regularization method for inclusions of the form $$T(x) \ni 0$$ where T is a set-valued mapping defined on a Banach space that enjoys metric regularity properties. We investigate, subsequently, the case when the mapping T is metrically regular, strongly metrically regular, strongly subregular and Lipschitz continuous and show the strong convergence of the solutions of regularized problems to a solution to the original inclusion $$T(x) \ni 0$$ . We also prove that the method has finite termination under some special conditioning assumptions on T and we study its stability with respect to some variational perturbations.

Journal

PositivitySpringer Journals

Published: Oct 28, 2008

References

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