WIAS Preprint No. 929, (2004)

Calmness of constraint systems with applications


  • Henrion, René
    ORCID: 0000-0001-5572-7213
  • Outrata, Jiří

2010 Mathematics Subject Classification

  • 90C30 49J53


  • calmness, constraint sets, nonsmooth calculus, value-at-risk




The paper is devoted to the analysis of the calmness property for constraint set mappings. After some general characterizations, specific results are obtained for various types of constraints, e.g., one single nonsmooth inequality, differentiable constraints modeled by polyhedral sets, finitely and infinitely many differentiable inequalities. The obtained conditions enable to detect calmness in a number of situations, where the standard criteria (via polyhedrality or the Aubin property) do not work. Their application in the framework of generalized differential calculus is explained and illustrated by examples associated with optimization and stability issues in connection with nonlinear complementarity problems or continuity of the value-at-risk.

Appeared in

  • Math. Program., 104 (2005) pp. 437--464.

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