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Convex print that page

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 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 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 preferences print that page

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 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 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 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 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