WIAS Preprint No. 710, (2002)

On the necessity of some constraint qualification conditions in convex programming


  • Tiba, Dan
  • Zălinescu, Constantin

2010 Mathematics Subject Classification

  • 49K27 90C25


  • convex function, constraint qualification, Lagrange multiplier, metric regularity, normal cone




In this paper, we realize a study of various constraint qualification conditions for the existence of Lagrange multipliers for convex minimization problems in general normed vector spaces, it is based on a new formula for the normal cone to the constraint set, on local metric regularity and a metric regularity property on bounded subsets. As a by-product, we obtain a characterization of the metric regularity of a finite family of closed convex sets.

Appeared in

  • J. Convex Anal., 11 (2004) pp. 95--110.

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