Stability of Saddle Points Via Explicit Coderivatives of Pointwise Subdifferentials

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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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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Keywords

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

Mathematics Subject Classification (2010)

  • 49J53
  • 49K40
  • 90C31