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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Vydáno v:	Set-valued and variational analysis Ročník 25; číslo 1; s. 69 - 112
Hlavní autoři:	Clason, Christian, Valkonen, Tuomo
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Dordrecht Springer Netherlands 01.03.2017 Springer Nature B.V
Témata:	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
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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.
AbstractList	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	Valkonen, Tuomo Clason, Christian
Author_xml	– sequence: 1 givenname: Christian surname: Clason fullname: Clason, Christian organization: Faculty of Mathematics, University Duisburg-Essen – sequence: 2 givenname: Tuomo surname: Valkonen fullname: Valkonen, Tuomo email: tuomo.valkonen@iki.fi organization: Department of Applied Mathematics and Theoretical Physics, University of Cambridge
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Snippet	We derive stability criteria for saddle points of a class of nonsmooth optimization problems in Hilbert spaces arising in PDE-constrained optimization, using...
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StartPage	69
SubjectTerms	Analysis Economic models Elliptic differential equations Functionals Hilbert space Mathematics Mathematics and Statistics Optimization Parameter identification Partial differential equations Saddle points Stability criteria
Title	Stability of Saddle Points Via Explicit Coderivatives of Pointwise Subdifferentials
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