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