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Convex hull print that page

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 . The convex hull also has a linear-algebraic characterization: The convex hull of  X is the set of all convex combinations of points in

wikipedia.org | 2011/8/10 6:57:43

Convex polytope print that page

A convex polytope is a special case of a polytope , having the additional property that it is also a convex set of points in the n -dimensional space R n . [ 1 ] Some authors use the terms convex polytope" and convex polyhedron" interchangeably, while others prefer to draw a distinction

wikipedia.org | 2011/4/16 5:21:07

Convex combination print that page

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 non-negative and sum up to 1. All possible convex combinations will be within the convex hull of the given points. In fact

wikipedia.org | 2010/9/26 19:39:52

Convex analysis print that page

Convex analysis From Wikipedia, the free encyclopedia Jump to: navigation , search 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

wikipedia.org | 2011/2/27 10:07:04

Convex conjugate print that page

In mathematics , convex conjugation is a generalization of the Legendre transformation . It is also known as Legendre–Fenchel transformation or Fenchel transformation (after Adrien-Marie Legendre and Werner Fenchel ). Contents 1 Definition 2 Examples 2.1 Connection with

wikipedia.org | 2011/9/17 21:00:32

Convex hull algorithms print that page

Algorithms that construct convex hulls of various objects have a broad range of applications in mathematics and computer science , see " Convex hull applications ". In computational geometry , numerous algorithms are proposed for computing the convex hull of a finite set of points, with

wikipedia.org | 2010/9/26 1:07:00

Convex function print that page

In mathematics , a real-valued function f ( x ) defined on an interval is called convex (or convex downward or concave upward ) 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 (the set

wikipedia.org | 2011/8/6 2:11:45

Polytope print that page

approaches to definition 2 Elements 3 Special classes of polytope 3.1 Regular polytopes 3.2 Convex polytopes 3.3 Star polytopes 3.4 Abstract polytopes 3.5 Self-dual polytopes 4 History 5 Uses 6 See also 7 References 8 External links [ edit ] Different approaches

wikipedia.org | 2011/4/25 3:23:04

Convex geometry print that page

The phrase convex geometry is also used in combinatorics as the name for an abstract model of convex sets based on antimatroids . Historical note Convex geometry is a relatively young mathematical discipline. Although the first known contributions to convex geometry date back to antiquity

wikipedia.org | 2011/9/3 1:52:47

Convex optimization print that page

defined on a convex subset of X , the problem is to find a point in for which the number f ( x ) is smallest, i.e., a point such that for all . The convexity of and f makes the powerful tools of convex analysis applicable: the Hahn–Banach theorem and the theory of subgradients

wikipedia.org | 2011/9/16 0:34:00