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Calmness of constraint systems with applications

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Abstract

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 the detection of 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.

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Authors and Affiliations

  1. Weierstrass Institute Berlin, D-10117, Berlin, Germany

    René Henrion

  2. Institute of Information Theory and Automation, 18208, Prague, Czech Republic

    Jiří V. Outrata

Authors
  1. René Henrion
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  2. Jiří V. Outrata
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Correspondence to Jiří V. Outrata.

Additional information

This research was supported by the DFG Research center Matheon Mathematics for key technologies in Berlin

Support by grant IAA1030405 of the Grant Agency of the Academy of Sciences of the Czech Republic is acknowledged

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Henrion, R., Outrata, J. Calmness of constraint systems with applications. Math. Program. 104, 437–464 (2005). https://doi.org/10.1007/s10107-005-0623-2

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  • DOI: https://doi.org/10.1007/s10107-005-0623-2

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