Work

A bilevel approach for parameter learning in inverse problems

Year: 2018

Type: article

Abstract: A learning approach for selecting regularization parameters in multi-penalty Tikhonov regularization is investigated. It leads to a bilevel optimization problem, where the lower level problem is a Tikhonov regularized problem parameterized in the regularization parameters. Conditions which ensure the existence of solutions to the bilevel optimization problem are derived, and these conditions are verified for two relevant examples. Difficulties arising from the possible lack of convexity of the lower level problems are discussed. Optimality conditions are given provided that a reasonable constraint qualification holds. Finally, results from numerical experiments used to test the developed theory are presented.

Source: Inverse Problems

DOI: 10.1088/1361-6420/aade77

Authors: Gernot Holler, Karl Kunisch, Richard C Barnard

Institutions: University of Graz, Austrian Academy of Sciences, Johann Radon Institute for Computational and Applied Mathematics, Oak Ridge National Laboratory

Language: English

Topic: Numerical methods in inverse problems

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,325

OpenAlex ID: W2786435781

FWCI: 3.654

Cites: 22

Cited by: 31

Related to: