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Journal of Convex Analysis 11 (2004), No. 1, 095--110
Copyright Heldermann Verlag 2004

On the Necessity of some Constraint Qualification Conditions in Convex Programming

Dan Tiba
Institute of Mathematics, Romanian Academy of Sciences, P.O. Box 1-764, 70700 Bucharest, Romania,

Constantin Zalinescu
University "Al. I. Cuza", Faculty of Mathematics, Bd. Copou Nr. 11, 6600 Iasi, Romania,

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.

Keywords: convex function, constraint qualification, Lagrange multiplier, metric regularity, normal cone.

MSC 2000: 49K27, 90C25.

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