Convex

A convex set.

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 set
• Convex polytope, a polytope which forms a convex set. These include convex polygons.
• Convex hull, the minimal convex set containing a set of points X
• Convex combination, a linear combination of points with non-negative coefficients that sum up to 1
• Convex conjugate, a generalization of the Legendre transformation
• Convex bipartite graph, a special kind of bipartite graph
• Convex plane graph, a plane graph with convex faces
• Convex optimization

Economics:

• Convexity in economics
• Convex preferences, a preference relation with convex upper contour sets
• Non-convexity (economics)

Finance:

• Bond convexity, a measure of the sensitivity of the price of a bond to changes in interest rates
• Convexity (finance), second derivatives in financial modeling generally

Optics:

• Convex lens, a lens with surfaces that curve outward

Art:

• Convex and Concave, a lithograph print by the artist M. C. Escher

Proper names:

• Convex Computer, a company that produced a number of vector supercomputers, bought by HP in 1995
• Convex Software Library, a client-side open source solution for Internet Explorer which uses a hidden Java applet to process XForms
• Convex application, an iPhone/Ipad software created by Ergonotics to perform conversion.

See also

• List of convexity topics
• Obtuse angle

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