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An alternative formulation for a new closed cone constraint qualification. (English) Zbl 1105.46052
Summary: We give an alternative formulation for the so-called closed cone constraint qualification (CCCQ) related to a convex optimization problem in Banach spaces recently introduced in the literature. This new formulation allows to prove in a simple way that (CCCQ) is weaker than some generalized interior-point constraint qualifications given in the past. By means of some insights from the theory of conjugate duality we also show that strong duality still holds under some weaker hypotheses than the ones considered so far in the literature.
##### MSC:
 46N10 Applications of functional analysis in optimization and programming 52A41 Convex functions and convex programs (convex geometry) 90C25 Convex programming