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 Fréchet code...

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Bibliographic Details
Published in:arXiv.org
Main Authors: Clason, Christian, Valkonen, Tuomo
Format: Paper
Language:English
Published: Ithaca Cornell University Library, arXiv.org 10.02.2017
Subjects:
Economic models
Hilbert space
Optimization
Parameter identification
Partial differential equations
Saddle points
Stability criteria
ISSN:2331-8422
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 Fréchet 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.
Bibliography:SourceType-Working Papers-1
ObjectType-Working Paper/Pre-Print-1
content type line 50
ISSN:2331-8422
DOI:10.48550/arxiv.1509.06582