Stability of Saddle Points Via Explicit Coderivatives of Pointwise Subdifferentials

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 code...

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Bibliographic Details
Published in:Set-valued and variational analysis Vol. 25; no. 1; pp. 69 - 112
Main Authors: Clason, Christian, Valkonen, Tuomo
Format: Journal Article
Language:English
Published: Dordrecht Springer Netherlands 01.03.2017
Springer Nature B.V
Subjects:
Analysis
Economic models
Elliptic differential equations
Functionals
Hilbert space
Mathematics
Mathematics and Statistics
Optimization
Parameter identification
Partial differential equations
Saddle points
Stability criteria
90C31
49J53
49K40
Saddle points
Fréchet coderivatives
Aubin property
Metric regularity
Integral functionals
ISSN:1877-0533, 1877-0541
Online Access:Get full text
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Summary: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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ISSN:1877-0533
1877-0541
DOI:10.1007/s11228-016-0366-7