Facially Dual Complete (nice) Cones and Lexicographic Tangents
نویسنده
چکیده
We study the boundary structure of closed convex cones, with a focus on facially dual complete (nice) cones. These cones form a proper subset of facially exposed convex cones, and they behave well in the context of duality theory for convex optimization. Using the wellknown and very commonly used concept of tangent cones in nonlinear optimization, we introduce some new notions for exposure of faces of convex sets. Based on these new notions, we obtain some necessary conditions and some sufficient conditions for a cone to be facially dual complete using tangent cones and a new notion of lexicographic tangent cones (these are a family of cones obtained from a recursive application of the tangent cone concept). Lexicographic tangent cones are related to Nesterov’s lexicographic derivatives.
منابع مشابه
On the connection of facially exposed, and nice cones
A closed convex cone K is called nice, if the set K∗ + F⊥ is closed for all F faces of K, where K∗ is the dual cone of K, and F⊥ is the orthogonal complement of the linear span of F. The niceness property plays a role in the facial reduction algorithm of Borwein and Wolkowicz, and the question whether the linear image of a nice cone is closed also has a simple answer. We prove several character...
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