A connection between uniqueness of minimizers in Tikhonov-type regularization and Morozov-like discrepancy principles

Vinicius Albani; Adriano De Cezaro

doi:10.3934/ipi.2019012

Article Contents

2019, Volume 13, Issue 1: 211-229. Doi: 10.3934/ipi.2019012

This issue Previous Article Simultaneously recovering potentials and embedded obstacles for anisotropic fractional Schrödinger operators Next Article

A connection between uniqueness of minimizers in Tikhonov-type regularization and Morozov-like discrepancy principles

Vinicius Albani^1, , and
Adriano De Cezaro^2,

1.
Dept of Mathematics, Federal University of Santa Catarina, Campus Trindade, Florianopolis, SC 88.040-900, Brazil
2.
IMEF, Federal University of Rio Grande, Av. Italia km 8, Rio Grande, RS 96201-900, Brazil

* Corresponding author: Vinicius Albani
* Corresponding author: Vinicius Albani

Received: May 31, 2018

Revised: August 31, 2018

Published: December 2018

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Abstract

We state sufficient conditions for the uniqueness of minimizers of Tikhonov-type functionals. We further explore a connection between such results and the well-posedness of Morozov-like discrepancy principle. Moreover, we find appropriate conditions to apply such results to the local volatility surface calibration problem.

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Mathematics Subject Classification: Primary: 65J22, 47J06; Secondary: 35R30.

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