Convex
Encyclopedia
The word convex means curving out or bulging outward, as opposed to concave. Convex or convexity may refer to:
Mathematics:
- Convex setConvex setIn Euclidean space, an object is convex if for every pair of points within the object, every point on the straight line segment that joins them is also within the object...
, a set of points containing all line segments between each pair of its points - Convex functionConvex functionIn mathematics, a real-valued function f defined on an interval is called convex 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 is a convex set...
, a function with the epigraphEpigraph (mathematics)In mathematics, the epigraph of a function f : Rn→R is the set of points lying on or above its graph:and the strict epigraph of the function is:The set is empty if f \equiv \infty ....
forming a convex set - Convex polytopeConvex polytopeA 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 Rn...
, a polytope which forms a convex set. These include convex polygonConvex polygonIn geometry, a polygon can be either convex or concave .- Convex polygons :A convex polygon is a simple polygon whose interior is a convex set...
s. - Convex hullConvex hullIn 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 minimal convex set containing a set of points X - Convex combinationConvex combinationIn convex geometry, a convex combination is a linear combination of points where all coefficients are non-negative and sum up to 1....
, a linear combination of points with non-negative coefficients that sum up to 1 - Convex conjugateConvex conjugateIn mathematics, convex conjugation is a generalization of the Legendre transformation. It is also known as Legendre–Fenchel transformation or Fenchel transformation .- Definition :...
, a generalization of the Legendre transformation - Convex bipartite graphConvex bipartite graphIn the mathematical field of graph theory, a convex bipartite graph is a bipartite graph with specific properties.A bipartite graph, , is said to be convex over the vertex set U if U can be enumerated such that for all v ∈ V the vertices adjacent to v are consecutive.Convexity over V is...
, a special kind of bipartite graph - Convex plane graph, a plane graph with convex faces
- Convex optimization
Economics:
- Convexity in economicsConvexity in economicsConvexity is an important topic in economics. In the Arrow-Debreu model of general economic equilibrium, agents have convex budget sets and convex preferences: At equilibrium prices, the budget hyperplane supports the best attainable indifference curve. The profit function is the convex conjugate...
- Convex preferencesConvex preferencesIn 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"...
, a preference relation with convex upper contour sets - Non-convexity (economics)Non-convexity (economics)In economics, non-convexity refers to violations of the convexity assumptions of elementary economics. Basic economics textbooks concentrate on consumers with convex preferences and convex budget sets and on producers with convex production sets; for convex models, the predicted economic behavior...
Finance:
- Bond convexityBond convexityIn finance, convexity is a measure of the sensitivity of the duration of a bond to changes in interest rates, the second derivative of the price of the bond with respect to interest rates . In general, the higher the convexity, the more sensitive the bond price is to decreasing interest rates and...
, a measure of the sensitivity of the price of a bond to changes in interest rates - Convexity (finance)Convexity (finance)In mathematical finance, convexity refers to non-linearities in a financial model. In other words, if the price of an underlying variable changes, the price of an output does not change linearly, but depends on the second derivative of the modeling function...
, second derivatives in financial modeling generally
Optics:
- Convex lens, a lens with surfaces that curve outward
Art:
- Convex and ConcaveConvex and ConcaveConvex and Concave is a lithograph print by the Dutch artist M. C. Escher, first printed in March 1955.It depicts an ornate architectural structure with many stairs, pillars and other shapes...
, a lithograph print by the artist M. C. Escher
Proper names:
- Convex ComputerConvex ComputerConvex Computer Corporation was a company that developed, manufactured and marketed vector minisupercomputers and supercomputers for small-to-medium-sized businesses. Their later Exemplar series of parallel computing machines were based on the Hewlett-Packard PA-RISC microprocessors, and in 1995,...
, a company that produced a number of vector supercomputers, bought by HP in 1995 - Convex Software LibraryConvex Software LibraryThe Convex Software Library is an open source client-side library that runs as a hidden applet in a Web browser and provides XForms support for browsers that do not support the World Wide Web Consortium standard. It is a subproject of the Chiba Engine....
, 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.