## 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 . 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

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

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

**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

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

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

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

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

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

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