# American Institute of Mathematical Sciences

February  2019, 13(1): 211-229. doi: 10.3934/ipi.2019012

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

 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

Received  June 2018 Revised  September 2018 Published  December 2018

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.

Citation: Vinicius Albani, Adriano De Cezaro. A connection between uniqueness of minimizers in Tikhonov-type regularization and Morozov-like discrepancy principles. Inverse Problems & Imaging, 2019, 13 (1) : 211-229. doi: 10.3934/ipi.2019012
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