Abstract:

This article proposes a few tangent cones, which are relative to the constraint qualifications of optimization problems. With the upper and lower directional derivatives of an objective function, the characteristics of cones on the constraint qualifications are presented. The interrelations among the constraint qualifications, a few cones involved, and level sets of upper and lower directional derivatives are derived.

Key words: Constraint qualifications, upper directional derivatives, lower directional derivatives, strongly directional differentiable, concave functions