List of convexity topics - AbsoluteAstronomy.com

This is a list of convexity topics, by Wikipedia page.

Alpha blending
Barycentric coordinates
Barycentric coordinates
Barycentric can refer to:In astronomy,*Barycentric coordinates , coordinates defined by the common center of mass of two or more bodies*Barycentric Dynamical Time, a former time standard in the Solar system...
Borsuk's conjecture
Borsuk's conjecture
The Borsuk problem in geometry, for historical reasons incorrectly called a Borsuk conjecture, is a question in discrete geometry.-Problem:...
Bond convexity
Bond convexity
In finance, convexity is a measure of the sensitivity of the duration of a bond to changes in interest rates, the second derivative of the price of the bond with respect to interest rates . In general, the higher the convexity, the more sensitive the bond price is to decreasing interest rates and...
Carathéodory's theorem (convex hull)
Carathéodory's theorem (convex hull)
In convex geometry Carathéodory's theorem states that if a point x of Rd lies in the convex hull of a set P, there is a subset P′ of P consisting of d+1 or fewer points such that x lies in the convex hull of P′. Equivalently, x lies in an r-simplex with vertices in P, where r \leq d...
Choquet theory
Choquet theory
In mathematics, Choquet theory is an area of functional analysis and convex analysis created by Gustave Choquet. It is concerned with measures with support on the extreme points of a convex set C...
Closed convex function
Closed convex function
In mathematics, a convex function is called closed if its epigraph is a closed set.- Properties :A closed convex function f is the pointwise supremum of the collection of all affine functions h such that h≤f.- References :...
Concavity
Concave function
In mathematics, a concave function is the negative of a convex function. A concave function is also synonymously called concave downwards, concave down, convex upwards, convex cap or upper convex.-Definition:...
Convex analysis
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....
Convex combination
Convex combination
In convex geometry, a convex combination is a linear combination of points where all coefficients are non-negative and sum up to 1....
Convex and concave
Convex and Concave
Convex and Concave is a lithograph print by the Dutch artist M. C. Escher, first printed in March 1955.It depicts an ornate architectural structure with many stairs, pillars and other shapes...
Convex conjugate
Convex conjugate
In mathematics, convex conjugation is a generalization of the Legendre transformation. It is also known as Legendre–Fenchel transformation or Fenchel transformation .- Definition :...
Convex function
Convex function
In mathematics, a real-valued function f defined on an interval is called convex if the graph of the function lies below the line segment joining any two points of the graph. Equivalently, a function is convex if its epigraph is a convex set...
Convex geometry
Convex geometry
Convex geometry is the branch of geometry studying convex sets, mainly in Euclidean space.Convex sets occur naturally in many areas of mathematics: computational geometry, convex analysis, discrete geometry, functional analysis, geometry of numbers, integral geometry, linear programming,...
Convex hull
Convex hull
In mathematics, the convex hull or convex envelope for a set of points X in a real vector space V is the minimal convex set containing X....
Convex lens
Convex optimization
Convex polygon
Convex polygon
In geometry, a polygon can be either convex or concave .- Convex polygons :A convex polygon is a simple polygon whose interior is a convex set...
Convex set
Convex set
In Euclidean space, an object is convex if for every pair of points within the object, every point on the straight line segment that joins them is also within the object...
Epigraph (mathematics)
Epigraph (mathematics)
In mathematics, the epigraph of a function f : Rn→R is the set of points lying on or above its graph:and the strict epigraph of the function is:The set is empty if f \equiv \infty ....
Extreme point
Extreme point
In mathematics, an extreme point of a convex set S in a real vector space is a point in S which does not lie in any open line segment joining two points of S...
Fenchel conjugate
Fenchel's inequality
Fixed point theorems in infinite-dimensional spaces
Fixed point theorems in infinite-dimensional spaces
In mathematics, a number of fixed-point theorems in infinite-dimensional spaces generalise the Brouwer fixed-point theorem. They have applications, for example, to the proof of existence theorems for partial differential equations....
Gift wrapping algorithm
Gift wrapping algorithm
In computational geometry, the gift wrapping algorithm is an algorithm for computing the convex hull of a given set of points.-Planar case:In the two-dimensional case the algorithm is also known as Jarvis march, after R. A. Jarvis, who published it in 1973; it has O time complexity, where n is the...
Graham scan
Graham scan
The Graham scan is a method of computing the convex hull of a finite set of points in the plane with time complexity O. It is named after Ronald Graham, who published the original algorithm in 1972...
Hadwiger conjecture (combinatorial geometry)
Hadwiger conjecture (combinatorial geometry)
In combinatorial geometry, the Hadwiger conjecture states that any convex body in n-dimensional Euclidean space can be covered by 2n or fewer smaller bodies homothetic with the original body, and that furthermore, the upper bound of 2n is necessary iff the body is a parallelpiped...
Hadwiger's theorem
Hadwiger's theorem
In integral geometry , Hadwiger's theorem characterises the valuations on convex bodies in Rn. It was proved by Hugo Hadwiger.-Valuations:...
Helly's theorem
Helly's theorem
Helly's theorem is a basic result in discrete geometry describing the ways that convex sets may intersect each other. It was discovered by Eduard Helly in 1913, but not published by him until 1923, by which time alternative proofs by and had already appeared...
Hyperplane
Hyperplane
A hyperplane is a concept in geometry. It is a generalization of the plane into a different number of dimensions.A hyperplane of an n-dimensional space is a flat subset with dimension n − 1...
Indifference curve
Indifference curve
In microeconomic theory, an indifference curve is a graph showing different bundles of goods between which a consumer is indifferent. That is, at each point on the curve, the consumer has no preference for one bundle over another. One can equivalently refer to each point on the indifference curve...
Infimal convolute
Interval (mathematics)
Interval (mathematics)
In mathematics, a interval is a set of real numbers with the property that any number that lies between two numbers in the set is also included in the set. For example, the set of all numbers satisfying is an interval which contains and , as well as all numbers between them...
Jarvis march
Jensen's inequality
Jensen's inequality
In mathematics, Jensen's inequality, named after the Danish mathematician Johan Jensen, relates the value of a convex function of an integral to the integral of the convex function. It was proved by Jensen in 1906. Given its generality, the inequality appears in many forms depending on the context,...
Lagrange multiplier
Legendre transformation
Legendre transformation
In mathematics, the Legendre transformation or Legendre transform, named after Adrien-Marie Legendre, is an operation that transforms one real-valued function of a real variable into another...
Locally convex topological vector space
Locally convex topological vector space
In functional analysis and related areas of mathematics, locally convex topological vector spaces or locally convex spaces are examples of topological vector spaces which generalize normed spaces. They can be defined as topological vector spaces whose topology is generated by translations of ...
Mahler volume
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 German-English mathematician Kurt Mahler...
Minimal convex decomposition
Minkowski's theorem
Minkowski's theorem
In mathematics, Minkowski's theorem is the statement that any convex set in Rn which is symmetric with respect to the origin and with volume greater than 2n d contains a non-zero lattice point...
Mixed volume
Mixed volume
In mathematics, more specifically, in convex geometry, the mixed volume is a way to associate a non-negative number to an n-tuple of convex bodies in the n-dimensional space...
Mixture density
Mixture density
In probability and statistics, a mixture distribution is the probability distribution of a random variable whose values can be interpreted as being derived in a simple way from an underlying set of other random variables. In particular, the final outcome value is selected at random from among the...
Newton polygon
Newton polygon
In mathematics, the Newton polygon is a tool for understanding the behaviour of polynomials over local fields.In the original case, the local field of interest was the field of formal Laurent series in the indeterminate X, i.e. the field of fractions of the formal power series ringover K, where K...
Proper convex function
Proper convex function
In mathematical analysis and optimization, a proper convex function is a convex function f taking values in the extended real number line such thatf -\infty...
Radon's theorem
Radon's theorem
In geometry, Radon's theorem on convex sets, named after Johann Radon, states that any set of d + 2 points in Rd can be partitioned into two sets whose convex hulls intersect...
Separating axis theorem
Separating axis theorem
For objects lying in a plane , the separating axis theorem states that, given two convex shapes, there exists a line onto which their projections will be separate if and only if they are not intersecting. A line for which the objects have disjoint projections is called a separating axis...
Shapley–Folkman lemma
Shapley–Folkman lemma
In geometry and economics, the Shapley–Folkman lemma describes the Minkowski addition of sets in a vector space. Minkowski addition is defined as the addition of the sets' members: for example, adding the set consisting of the integers zero and one to itself yields the set consisting of...
Shephard's problem
Shephard's problem
In mathematics, Shephard's problem, is the following geometrical question asked by : if K and L are centrally symmetric convex bodies in n-dimensional Euclidean space such that whenever K and L are projected onto a hyperplane, the volume of the projection of K is smaller than the volume of the...
Simplex
Simplex
In geometry, a simplex is a generalization of the notion of a triangle or tetrahedron to arbitrary dimension. Specifically, an n-simplex is an n-dimensional polytope which is the convex hull of its n + 1 vertices. For example, a 2-simplex is a triangle, a 3-simplex is a tetrahedron,...
Simplex method
Subdifferential
Supporting hyperplane
Supporting hyperplane
Supporting hyperplane is a concept in geometry. A hyperplane divides a space into two half-spaces. A hyperplane is said to support a set S in Euclidean space \mathbb R^n if it meets both of the following:...
Supporting hyperplane theorem

The source of this article is wikipedia, the free encyclopedia. The text of this article is licensed under the GFDL.