Abstract
The variational form of mollification fits in an extension of the generalized Tikhonov regularization. Using tools from variational analysis, we prove asymptotic consistency results for both this extended framework and the particular form of mollification that one obtains when building on the notion of target object.
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Acknowledgements
The author wishes to thank Nathaël Alibaud for fruitful discussions on the subject, which led to significant improvements of this paper.
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Maréchal, P. (2021). A Note on Quadratic Penalties for Linear Ill-Posed Problems: From Tikhonov Regularization to Mollification. In: Laha, V., Maréchal, P., Mishra, S.K. (eds) Optimization, Variational Analysis and Applications. IFSOVAA 2020. Springer Proceedings in Mathematics & Statistics, vol 355. Springer, Singapore. https://doi.org/10.1007/978-981-16-1819-2_9
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DOI: https://doi.org/10.1007/978-981-16-1819-2_9
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