Set-Valued and Variational Analysis

, Volume 25, Issue 1, pp 69–112

Stability of Saddle Points Via Explicit Coderivatives of Pointwise Subdifferentials

Open Access
Article

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.

Keywords

Metric regularity Aubin property Saddle points Fréchet coderivatives Integral functionals 

Mathematics Subject Classification (2010)

49J53 49K40 90C31 

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© The Author(s) 2016

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Faculty of MathematicsUniversity Duisburg-EssenEssenGermany
  2. 2.Department of Applied Mathematics and Theoretical PhysicsUniversity of CambridgeCambridgeUK

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