Set-Valued and Variational Analysis

, Volume 25, Issue 1, pp 69–112 | Cite as

Stability of Saddle Points Via Explicit Coderivatives of Pointwise Subdifferentials

  • Christian Clason
  • Tuomo Valkonen
Open Access


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.


Metric regularity Aubin property Saddle points Fréchet coderivatives Integral functionals 

Mathematics Subject Classification (2010)

49J53 49K40 90C31 


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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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