Stability of Saddle Points Via Explicit Coderivatives of Pointwise Subdifferentials

Christian Clason; Tuomo Valkonen

doi:10.1007/s11228-016-0366-7

Stability of Saddle Points Via Explicit Coderivatives of Pointwise Subdifferentials

Christian Clason, Tuomo Valkonen

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

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.

Original language	English (US)
Pages (from-to)	69-112
Number of pages	44
Journal	Set-Valued and Variational Analysis
Volume	25
Issue number	1
DOIs	https://doi.org/10.1007/s11228-016-0366-7
State	Published - Mar 2 2016
Externally published	Yes

ASJC Scopus subject areas

Statistics and Probability
Numerical Analysis
Analysis
Applied Mathematics
Geometry and Topology

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10.1007/s11228-016-0366-7

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title = "Stability of Saddle Points Via Explicit Coderivatives of Pointwise Subdifferentials",

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.",

author = "Christian Clason and Tuomo Valkonen",

note = "KAUST 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.",

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doi = "10.1007/s11228-016-0366-7",

language = "English (US)",

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journal = "Set-Valued and Variational Analysis",

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TY - JOUR

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AU - Clason, Christian

AU - Valkonen, Tuomo

N1 - KAUST 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.

PY - 2016/3/2

Y1 - 2016/3/2

N2 - 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.

AB - 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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UR - http://link.springer.com/10.1007/s11228-016-0366-7

UR - http://www.scopus.com/inward/record.url?scp=85011886981&partnerID=8YFLogxK

U2 - 10.1007/s11228-016-0366-7

DO - 10.1007/s11228-016-0366-7

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EP - 112

JO - Set-Valued and Variational Analysis

JF - Set-Valued and Variational Analysis

IS - 1

ER -

Stability of Saddle Points Via Explicit Coderivatives of Pointwise Subdifferentials

Abstract

ASJC Scopus subject areas

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