# Category: Convex geometry

Symmetric cone
In mathematics, symmetric cones, sometimes called domains of positivity, are open convex self-dual cones in Euclidean space which have a transitive group of symmetries, i.e. invertible operators that
Equichordal point problem
In Euclidean plane geometry, the equichordal point problem is the question whether a closed planar convex body can have two equichordal points. The problem was originally posed in 1916 by Fujiwara and
Convex geometry
In mathematics, convex geometry is the branch of geometry studying convex sets, mainly in Euclidean space. Convex sets occur naturally in many areas: computational geometry, convex analysis, discrete
Convex cone
In linear algebra, a cone—sometimes called a linear cone for distinguishing it from other sorts of cones—is a subset of a vector space that is closed under scalar multiplication; that is, C is a cone
Tangent cone
In geometry, the tangent cone is a generalization of the notion of the tangent space to a manifold to the case of certain spaces with singularities.
Convex polygon
In geometry, a convex polygon is a polygon that is the boundary of a convex set. This means that the line segment between two points of the polygon is contained in the union of the interior and the bo
Face (geometry)
In solid geometry, a face is a flat surface (a planar region) that forms part of the boundary of a solid object; a three-dimensional solid bounded exclusively by faces is a polyhedron. In more technic
Convex metric space
In mathematics, convex metric spaces are, intuitively, metric spaces with the property any "segment" joining two points in that space has other points in it besides the endpoints. Formally, consider a
Convexity in economics
Convexity is an important topic in economics. In the Arrow–Debreu model of general economic equilibrium, agents have convex budget sets and convex preferences: At equilibrium prices, the budget hyperp
Convex curve
In geometry, a convex curve is a plane curve that has a supporting line through each of its points.Examples of convex curves include the boundaries of convex sets and the graphs of convex functions. I
Busemann–Petty problem
In the mathematical field of convex geometry, the Busemann–Petty problem, introduced by Herbert Busemann and , asks whether it is true that a symmetric convex body with larger central hyperplane secti
In geometry, the Minkowski sum (also known as dilation) of two sets of position vectors A and B in Euclidean space is formed by adding each vector in A to each vector in B, i.e., the set Analogously,
Dual cone and polar cone
Dual cone and polar cone are closely related concepts in convex analysis, a branch of mathematics.
Dykstra's projection algorithm
Dykstra's algorithm is a method that computes a point in the intersection of convex sets, and is a variant of the alternating projection method (also called the projections onto convex sets method). I
Convex analysis
Convex analysis is the branch of mathematics devoted to the study of properties of convex functions and convex sets, often with applications in convex minimization, a subdomain of optimization theory.
Conical combination
Given a finite number of vectors in a real vector space, a conical combination, conical sum, or weighted sum of these vectors is a vector of the form where are non-negative real numbers. The name deri
B-convex space
In functional analysis, the class of B-convex spaces is a class of Banach space. The concept of B-convexity was defined and used to characterize Banach spaces that have the strong law of large numbers
List of convexity topics
This is a list of convexity topics, by Wikipedia page. * Alpha blending - the process of combining a translucent foreground color with a background color, thereby producing a new blended color. This
Bond convexity
In finance, bond convexity is a measure of the non-linear relationship of bond prices to changes in interest rates, the second derivative of the price of the bond with respect to interest rates (durat
Shapley–Folkman lemma
The Shapley–Folkman lemma is a result in convex geometry with applications in mathematical economics that describes the Minkowski addition of sets in a vector space. Minkowski addition is defined as t
Convexity (finance)
In mathematical finance, convexity refers to non-linearities in a financial model. In other words, if the price of an underlying variable changes, the price of an output does not change linearly, but
Blaschke sum
In convex geometry and the geometry of convex polytopes, the Blaschke sum of two polytopes is a polytope that has a facet parallel to each facet of the two given polytopes, with the same measure. When
Absolutely convex set
In mathematics, a subset C of a real or complex vector space is said to be absolutely convex or disked if it is convex and balanced (some people use the term "circled" instead of "balanced"), in which
Antimatroid
In mathematics, an antimatroid is a formal system that describes processes in which a set is built up by including elements one at a time, and in which an element, once available for inclusion, remain
Projection body
In convex geometry, the projection body of a convex body in n-dimensional Euclidean space is the convex body such that for any vector , the support function of in the direction u is the (n – 1)-dimens
Non-convexity (economics)
In economics, non-convexity refers to violations of the convexity assumptions of elementary economics. Basic economics textbooks concentrate on consumers with convex preferences (that do not prefer ex
Supporting hyperplane
In geometry, a supporting hyperplane of a set in Euclidean space is a hyperplane that has both of the following two properties: * is entirely contained in one of the two closed half-spaces bounded by
Gilbert–Johnson–Keerthi distance algorithm
The Gilbert–Johnson–Keerthi distance algorithm is a method of determining the minimum distance between two convex sets. Unlike many other distance algorithms, it does not require that the geometry dat
Strictly convex set
No description available.
Difference bound matrix
In model checking, a field of computer science, a difference bound matrix (DBM) is a data structure used to represent some convex polytopes called zones. This structure can be used to efficiently impl
Convex polytope
A convex polytope is a special case of a polytope, having the additional property that it is also a convex set contained in the -dimensional Euclidean space . Most texts use the term "polytope" for a
John ellipsoid
In mathematics, the John ellipsoid or Löwner-John ellipsoid E(K) associated to a convex body K in n-dimensional Euclidean space Rn can refer to the n-dimensional ellipsoid of maximal volume contained
Projections onto convex sets
In mathematics, projections onto convex sets (POCS), sometimes known as the alternating projection method, is a method to find a point in the intersection of two closed convex sets. It is a very simpl
Betavexity
In investment analysis, betavexity is a form of convexity that is specific to the beta coefficient of a long tailed investment (i.e. mortality risk). It is similar in nature to bond convexity or gamma
Exposed point
In mathematics, an exposed point of a convex set is a point at which some continuous linear functional attains its strict maximum over . Such a functional is then said to expose . There can be many ex
Mixed volume
In mathematics, more specifically, in convex geometry, the mixed volume is a way to associate a non-negative number to an -tuple of convex bodies in -dimensional space. This number depends on the size
Support function
In mathematics, the support function hA of a non-empty closed convex set A in describes the (signed) distances of supporting hyperplanes of A from the origin. The support function is a convex function
Region (model checking)
In model checking, a field of computer science, a region is a convex polytope in for some dimension , and more precisely a zone, satisfying some minimality property. The regions partition . The set of
Convex combination
In convex geometry and vector algebra, a convex combination is a linear combination of points (which can be vectors, scalars, or more generally points in an affine space) where all coefficients are no
Convexity correction
No description available.
Extreme point
In mathematics, an extreme point of a convex set in a real or complex vector space is a point in which does not lie in any open line segment joining two points of In linear programming problems, an ex
Blunt cone (mathematics)
No description available.
Lens (geometry)
In 2-dimensional geometry, a lens is a convex region bounded by two circular arcs joined to each other at their endpoints. In order for this shape to be convex, both arcs must bow outwards (convex-con
Minkowski Portal Refinement
The Minkowski Portal Refinement collision detection algorithm is a technique for determining whether two convex shapes overlap. The algorithm was created by in 2006 and was first published in Game Pro
Convex Polytopes
Convex Polytopes is a graduate-level mathematics textbook about convex polytopes, higher-dimensional generalizations of three-dimensional convex polyhedra. It was written by Branko Grünbaum, with cont
Rotating calipers
In computational geometry, the method of rotating calipers is an algorithm design technique that can be used to solve optimization problems including finding the width or diameter of a set of points.
Mahler volume
In convex geometry, the Mahler volume of a centrally symmetric convex body is a dimensionless quantity that is associated with the body and is invariant under linear transformations. It is named after
Shephard's problem
In mathematics, Shephard's problem, is the following geometrical question asked by Geoffrey Colin Shephard in 1964: if K and L are centrally symmetric convex bodies in n-dimensional Euclidean space su
Convex set
In geometry, a subset of a Euclidean space, or more generally an affine space over the reals, is convex if, given any two points in the subset, the subset contains the whole line segment that joins th
Klee–Minty cube
The Klee–Minty cube or Klee–Minty polytope (named after Victor Klee and George J. Minty) is a unit hypercube of variable dimension whose corners have been perturbed. Klee and Minty demonstrated that G