Stability of saddle points via explicit coderivatives of pointwise subdifferentials
Published version
Peer-reviewed
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Authors
Clason, Christian
Valkonen, Tuomo
Abstract
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.
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Keywords
4901 Applied Mathematics, 4903 Numerical and Computational Mathematics, 49 Mathematical Sciences
Journal Title
Set-Valued and Variational Analysis volume
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Journal ISSN
1877-0533
1877-0541
1877-0541
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Publisher
Springer
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Sponsorship
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).