A Note on the Morozov Principle via Lagrange Duality
| Autor: | Pierre Maréchal, Xavier Bonnefond, Walter Cedric Simo Tao Lee |
|---|---|
| Přispěvatelé: | Institut de Mathématiques de Toulouse UMR5219 (IMT), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS) |
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
Statistics and Probability
Numerical Analysis Lagrange duality Applied Mathematics Nonparametric statistics Duality (optimization) 010103 numerical & computational mathematics Maximization 01 natural sciences Regularization (mathematics) Regression Tikhonov regularization 010104 statistics & probability [MATH.MATH-GM]Mathematics [math]/General Mathematics [math.GM] Applied mathematics Geometry and Topology 0101 mathematics Noise level Analysis ComputingMilieux_MISCELLANEOUS Mathematics |
| Zdroj: | Set-Valued and Variational Analysis Set-Valued and Variational Analysis, Springer, 2018, 26 (2), pp.265-275 Set-Valued and Variational Analysis, 2018, 26 (2), pp.265-275 |
| ISSN: | 1877-0533 1877-0541 |
| Popis: | Considering a general linear ill-posed equation, we explore the duality arising from the requirement that the discrepancy should take a given value based on the estimation of the noise level, as is notably the case when using the Morozov principle. We show that, under reasonable assumptions, the dual function is smooth, and that its maximization points out the appropriate value of Tikhonov’s regularization parameter. The numerical relevance of our approach is established by means of an illustrative example from nonparametric instrumental regression, a standard problem in statistics. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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