We derive stability criteria for saddle points of a class of nonsmooth optimization problems in Hilbert spaces arising in PDE-constrained optimization, using metric regularity of infinite-dimensional set-valued mappings. A main ingredient is an explicit pointwise characterization of the regular coderivative of the subdifferential of convex integral functionals. This is applied to several stability properties for parameter identification problems for an elliptic partial differential equation with non-differentiable data fitting terms.
Bibliographical noteKAUST Repository Item: Exported on 2021-04-02
Acknowledged KAUST grant number(s): KUK-I1-007-43
Acknowledgements: In Cambridge, T. Valkonen has been supported by the King Abdullah University of Science and Technology (KAUST) Award No. KUK-I1-007-43, and EPSRC grants Nr. EP/J009539/1 “Sparse & Higher-order Image Restoration”, and Nr. EP/M00483X/1 “Efficient computational tools for inverse imaging problems”. While in Quito, T. Valkonen has moreover been supported by a Prometeo scholarship of the Senescyt (Ecuadorian Ministry of Science, Technology, Education, and Innovation).
This publication acknowledges KAUST support, but has no KAUST affiliated authors.
ASJC Scopus subject areas
- Statistics and Probability
- Numerical Analysis
- Applied Mathematics
- Geometry and Topology