WIAS Preprint No. 685, (2001)

On calmness of a class of multifunctions


  • Henrion, René
  • Jourani, Abderrahim
  • Outrata, Jiří

2010 Mathematics Subject Classification

  • 90C31 49J52


  • calmness, multifunctions, constraint qualifications, nonsmooth calculus, solution stability, equilibrium problems, weak sharp minima


The paper deals with calmness of a class of multifunctions in finite dimensions. Its first part is devoted to various calmness criteria which are derived in terms of coderivatives and subdifferentials. The second part demonstrates the importance of calmness in several areas of nonsmoooth 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.

Appeared in

  • SIAM Journal on Optimization, 13 (2002) pp. 603-618

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