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Stability of Saddle Points Via Explicit Coderivatives of Pointwise Subdifferentials

Set-Valued and Variational Analysis volume 25, pages 69–112 (2017)Cite this 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.

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Author information

Authors and Affiliations

  1. Faculty of Mathematics, University Duisburg-Essen, 45117, Essen, Germany

    Christian Clason

  2. Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, UK

    Tuomo Valkonen

Authors
  1. Christian Clason
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  2. Tuomo Valkonen
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Correspondence to Tuomo Valkonen.

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Clason, C., Valkonen, T. Stability of Saddle Points Via Explicit Coderivatives of Pointwise Subdifferentials. Set-Valued Var. Anal 25, 69–112 (2017). https://doi.org/10.1007/s11228-016-0366-7

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  • DOI: https://doi.org/10.1007/s11228-016-0366-7

Keywords

  • Metric regularity
  • Aubin property
  • Saddle points
  • Fréchet coderivatives
  • Integral functionals

Mathematics Subject Classification (2010)

  • 49J53
  • 49K40
  • 90C31