## Convex

The word **convex** means curving out or bulging outward , as opposed to concave . **Convex** or convexity may refer to: Mathematics : **Convex** set , a set of points containing all line segments between each pair of its points **Convex** function , a function with the epigraph forming a **convex**

**wikipedia.org**| 2011/4/6 12:47:25

## 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 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 preferences

In economics , **convex** preferences refer to a property of an individual's ordering of various outcomes which roughly corresponds to the idea that "averages are better than the extremes". The concept roughly corresponds to the "law" of diminishing marginal utility but uses modern theory to

**wikipedia.org**| 2011/3/7 1:37:39

## 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 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 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 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