On strongly E-convex sets and strongly E-convex cone sets
نویسندگان
چکیده
منابع مشابه
Local characterization of strongly convex sets
Strongly convex sets in Hilbert spaces are characterized by local properties. One quantity which is used for this purpose is a generalization of the modulus of convexity δΩ of a set Ω. We also show that limε→0 δΩ(ε)/ε 2 exists whenever Ω is closed and convex.
متن کاملAsymptotics of Convex Sets in E
A. We study convex sets C of finite (but non-zero) volume inH andE.Weshowthat the intersectionC∞ of any such setwith the ideal boundary of H has Minkowski (and thus Hausdorff) dimension of at most (n − 1)/2. and this bound is sharp, at least in some dimensions n. We also show a sharp bound when C∞ is a smooth submanifold of ∂∞H. In the hyperbolic case, we show that for any k ≤ (n− 1)/2 t...
متن کاملStrongly normal sets of convex polygons or polyhedra
A set V of nondegenerate convex polygons P in R, or polyhedra P in R, will be called normal if the intersection of any two of the P's of V is a face (in the case of polyhedra), an edge, a vertex, or empty. V is called strongly normal (SN) if it is normal and, for all P, Pi,..., Pn, if each P; intersects P and / = Px f) ... f~l Pn is nonempty, then I intersects P. The union of the Pt€ V that int...
متن کاملOn the quadratic support of strongly convex functions
In this paper, we first introduce the notion of $c$-affine functions for $c> 0$. Then we deal with some properties of strongly convex functions in real inner product spaces by using a quadratic support function at each point which is $c$-affine. Moreover, a Hyers–-Ulam stability result for strongly convex functions is shown.
متن کاملLifts of Convex Sets and Cone Factorizations
In this paper we address the basic geometric question of when a given convex set is the image under a linear map of an affine slice of a given closed convex cone. Such a representation or “lift” of the convex set is especially useful if the cone admits an efficient algorithm for linear optimization over its affine slices. We show that the existence of a lift of a convex set to a cone is equival...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Al-Qadisiyah for computer science and mathematics
سال: 2019
ISSN: 2521-3504,2074-0204
DOI: 10.29304/jqcm.2019.11.1.459