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Zbl 1028.49018
Henrion, René; Jourani, Abderrahim; Outrata, Jiri
On the calmness of a class of multifunctions. (English)
[J] SIAM J. Optim. 13, No.2, 603-618 (2002). ISSN 1052-6234; ISSN 1095-7189/e

Summary: The paper deals with the calmness of a class of multifunctions in finite dimensions. Its first part is devoted to various conditions for calmness, which are derived in terms of coderivatives and subdifferentials. The second part demonstrates the importance of calmness in several areas of nonsmooth analysis. In particular, we focus on nonsmooth calculus and solution stability in mathematical programming and in equilibrium problems. The derived conditions find a number of applications there.

MSC 2000:: *49J52 Nonsmooth analysis (other weak concepts of optimality)
49J53 Set-valued and variational analysis
90C31 Sensitivity, etc.
49K40 Sensitivity of optimal solutions in the presence of perturbations
26E25 Set-valued real functions

Keywords: calmness; multifunctions; constraint qualifications; nonsmooth calculus; solution stability; equilibrium problems; weak sharp minima

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