Carathéodory's theorem is a theorem in convex geometry. It states that if a point x {\displaystyle x} lies in the convex hull C o n v ( P ) {\displaystyle...

boundary Carathéodory's theorem (convex hull), about the convex hulls of sets in R d {\displaystyle \mathbb {R} ^{d}} Carathéodory's existence theorem, about...

In geometry, the convex hull, convex envelope or convex closure of a shape is the smallest convex set that contains it. The convex hull may be defined either...

convexity Convex cone Convex series Convex metric space Carathéodory's theorem (convex hull) Choquet theory Helly's theorem Holomorphically convex hull Integrally-convex...

Banach–Alaoglu theorem – Theorem in functional analysis Carathéodory's theorem (convex hull) – Point in the convex hull of a set P in Rd, is the convex combination...

learning resources about Convex combination Affine hull Carathéodory's theorem (convex hull) Simplex Barycentric coordinate system Convex space Rockafellar,...

Carathéodory's theorem in convex geometry states that if a point x {\displaystyle x} of R d {\displaystyle \mathbb {R} ^{d}} lies in the convex hull of...

geometry Conical hull, in convex geometry Convex hull, in convex geometry Carathéodory's theorem (convex hull) Holomorphically convex hull, in complex analysis...

vector is in the cone might be exponentially long. Fortunately, Carathéodory's theorem guarantees that every vector in the cone can be represented by at...

r subsets whose convex hulls intersect in at least one common point. Carathéodory's theorem states that any point in the convex hull of some set of points...

Helly's theorem is a basic result in discrete geometry on the intersection of convex sets. It was discovered by Eduard Helly in 1913, but not published...

basic form of convexity in finance. Carathéodory's theorem (convex hull) - If a point x of Rd lies in the convex hull of a set P, there is a subset of P...

orthogonal convex hull of such point set is equal to the point set itself. A well known property of convex hulls is derived from the Carathéodory's theorem: A...

Several variations of Carathéodory's theorem (convex hull) on the enclosure of points in the convex hulls of other points Steinitz's theorem (field theory) on...

necessarily normable, the existence of a convex local base for the zero vector is strong enough for the Hahn–Banach theorem to hold, yielding a sufficiently rich...

points. Carathéodory's theorem – Point in the convex hull of a set P in Rd, is the convex combination of d+1 points in P Helly's theorem – Theorem about...

vector is in the polytope might be exponentially long. Fortunately, Carathéodory's theorem guarantees that every vector in the polytope can be represented...

the Shapley–Folkman theorem provides an upper bound on the distance between any point in the Minkowski sum and its convex hull. This upper bound is sharpened...

intersections of convex hulls. However, Helly's theorem, Carathéodory's theorem, and Radon's theorem all postdate Kirchberger's theorem. A strengthened...

point in P, write it as a convex combination of at most n vertices of P (an algorithmic version of Carathéodory's theorem). Separation oracle - an algorithm...

any I ⊆ { 1 , … , n } {\displaystyle I\subseteq \{1,\ldots ,n\}} , the convex hull of the vertices corresponding to I {\displaystyle I} is covered by ⋃...

operator) Oriented matroids (realizable OMs and applications) Carathéodory's theorem (convex hull) Lemma of Farkas Monotropic programming Tucker, Albert W...

Radon measures on X, equipped with its vague topology. Moreover, the convex hull of the image of X under this embedding is dense in the space of probability...

theory of convex polytopes, zonotopes, and configurations of vectors (equivalently, arrangements of hyperplanes). Many results—Carathéodory's theorem, Helly's...

mathematics, a cyclic polytope, denoted C(n, d), is a convex polytope formed as a convex hull of n distinct points on a rational normal curve in Rd,...

set, and cone denotes the conic hull. The set cone(E) is also called the recession cone of P.: 10  Carathéodory's theorem states that, if P is a d-dimensional...

discrete geometry covered by this book include: Carathéodory's theorem that every point in the convex hull of a planar set belongs to a triangle determined...