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Facially Dual Complete (Nice) cones and lexicographic tangents. (arXiv:1704.06368v1 [math.OC])
来源于:arXiv
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 well-known 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. 查看全文>>