Approximately convex average sums of unbounded sets
نویسندگان
چکیده
منابع مشابه
Finite Illumination of Unbounded Closed Convex Sets
If K is an unbounded closed convex subset of Ed having nonempty interior, we seek necessary and/or sufficient conditions to ensure that the boundary of K can be externally illuminated from a finite set of directions. This problem was stated as open in a recent book by Boltyanski. The tools used in this search are those developed by Visibility Theory such as the ideas of star, inner stem, visibi...
متن کاملUnbounded Convex Semialgebraic Sets as Spectrahedral Shadows
Recently, Helton and Nie [3] showed that a compact convex semialgebraic set S is a spectrahedral shadow if the boundary of S is nonsingular and has positive curvature. In this paper, we generalize their result to unbounded sets, and also study the effect of the perspective transform on singularities.
متن کاملUnbounded convex sets for non-convex mixed-integer quadratic programming
This paper introduces a fundamental family of unbounded convex sets that arises in the context of non-convex mixed-integer quadratic programming. It is shown that any mixed-integer quadratic program with linear constraints can be reduced to the minimisation of a linear function over a set in the family. Some fundamental properties of the convex sets are derived, along with connections to some o...
متن کاملOn the Size of Approximately Convex Sets in Normed Spaces
Let X be a normed space. A set A ⊆ X is approximately convex if d(ta + (1 − t)b, A) ≤ 1 for all a, b ∈ A and t ∈ [0, 1]. We prove that every n-dimensional normed space contains approximately convex sets A with H(A,Co(A)) ≥ log2 n− 1 and diam(A) ≤ C √ n(lnn), where H denotes the Hausdorff distance. These estimates are reasonably sharp. For every D > 0, we construct worst possible approximately c...
متن کاملUniquely Remotal Sets in $c_0$-sums and $ell^infty$-sums of Fuzzy Normed Spaces
Let $(X, N)$ be a fuzzy normed space and $A$ be a fuzzy boundedsubset of $X$. We define fuzzy $ell^infty$-sums and fuzzy $c_0$-sums offuzzy normed spaces. Then we will show that in these spaces, all fuzzyuniquely remotal sets are singletons.
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: Proceedings of the American Mathematical Society
سال: 1974
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1974-0338928-8