WIAS Preprint No. 553, (2000)

A subdifferential criterion for calmness of multifunctions


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

2010 Mathematics Subject Classification

  • 90C31 26E25 49J52


  • calmness, multifunctions, coderivative, constraint sets, nonlinear complementarity problems




A criterion for the calmness of a class of multifunctions between finite-dimensional spaces is derived in terms of subdifferential concepts developed by Mordukhovich. The considered class comprises general constraint set mappings as they occur in optimization or mappings associated with a certain type of variational systems. The criterion for calmness is obtained as an appropriate reduction of Mordukhovich's well-known characterization of the stronger Aubin property (roughly spoken, one may pass to the boundaries of normal cones or subdifferentials when aiming at calmness).

Appeared in

  • Journal of Mathematical Analysis and Applications 258 (2001), pp. 110-130

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