On the Necessity of some Constraint Qualiflcation Conditions in Convex Programming
Dan Tiba, Constantin Zălinescu · 2004
In this paper we realize a study of various constraint qualiflcation 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 flnite family of closed convex sets.