WIAS Preprint No. 645, (2001)

Boundary-oriented subdifferential characterization of calmness for convex systems


  • Henrion, René
    ORCID: 0000-0001-5572-7213
  • Jourani, Abderrahim

2010 Mathematics Subject Classification

  • 90C31 26E25 49J52


  • calmness, multifunctions, convex systems, constraint qualifications




We study subdifferential characterizations of the calmness property for multifunctions representing convex constraint systems in a Banach space. Extending earlier work in finite dimensions, we show that - in contrast to the stronger Aubin property of a multifunction (or metric regularity of its inverse), calmness can be ensured by corresponding weaker constraint qualifications which are based on boundaries of subdifferentials and normal cones only rather than on the full objects.

Appeared in

  • SIAM Journal on Optimization, 13 (2002) 520-534, under new title: Subdifferential Conditions for Calmness of Convex Constraints.

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