This is a list of convexity topics, by Wikipedia page.
Alpha blending - the process of combining a translucent foreground color with a background color, thereby producing a new blended color. This is a convex combination of two colors allowing for transparency effects in computer graphics.
Barycentric coordinates - a coordinate system in which the location of a point of a simplex (a triangle, tetrahedron, etc.) is specified as the center of mass, or barycenter, of masses placed at its vertices. The coordinates are non-negative for points in the convex hull.
Borsuk's conjecture - a conjecture about the number of pieces required to cover a body with a larger diameter. Solved by Hadwiger for the case of smooth convex bodies.
Bond convexity - a measure of the non-linear relationship between price and yield duration of a bond to changes in interest rates, the second derivative of the price of the bond with respect to interest rates. A basic form of convexity in finance.
Carathéodory's theorem (convex hull) - If a point x of Rd lies in the convex hull of a set P, there is a subset of P with d+1 or fewer points such that x lies in its convex hull.
Choquet theory - an area of functional analysis and convex analysis concerned with measures with support on the extreme points of a convex set C. Roughly speaking, all vectors of C should appear as 'averages' of extreme points.
Complex convexity — extends the notion of convexity to complex numbers.
Convex analysis - the branch of mathematics devoted to the study of properties of convex functions and convex sets, often with applications in convex minimization.
Convex combination - a linear combination of points where all coefficients are non-negative and sum to 1. All convex combinations are within the convex hull of the given points.
Convex and concave - a print by Escher in which many of the structure's features can be seen as both convex shapes and concave impressions.
Convex body - a compact convex set in a Euclidean space whose interior is non-empty.
Convex conjugate - a dual of a real functional in a vector space. Can be interpreted as an encoding of the convex hull of the function's epigraph in terms of its supporting hyperplanes.
Convex curve - a curve that lies entirely on one side of each of its tangents. The interior of a convex curve is a convex set.
Convex function - a function in which the line segment between any two points on the graph of the function lies above the graph.
Closed convex function - a convex function whose every the sublevel set is a closed set.
Proper convex function - a convex function whose effective domain is nonempty and it never attains minus infinity.
Concave function - the negative of a convex function.
Convex geometry - the branch of geometry studying convex sets, mainly in Euclidean space. Contains three sub-branches: general convexity, polytopes and polyhedra, and discrete geometry.
Convex hull (aka convex envelope) - the smallest convex set that contains a given set of points in Euclidean space.
Convex lens - a lens in which one or two sides is curved or bowed outwards. Light passing through the lens is converged (or focused) to a spot behind the lens.
Convex optimization - a subfield of optimization, studies the problem of minimizing convex functions over convex sets. The convexity property can make optimization in some sense "easier" than the general case - for example, any local minimum must be a global minimum.
Convex polygon - a 2-dimensional polygon whose interior is a convex set in the Euclidean plane.
Convex polytope - an n-dimensional polytope which is also a convex set in the Euclidean n-dimensional space.
Convex set - a set in Euclidean space in which contains every segment between every two of its points.
Convexity (finance) - refers to non-linearities in a financial model. When the price of an underlying variable changes, the price of an output does not change linearly, but depends on the higher-order derivatives of the modeling function. Geometrically, the model is no longer flat but curved, and the degree of curvature is called the convexity.
Epigraph (mathematics)
Extreme point
Fenchel conjugate
Fenchel's inequality
Fixed point theorems in infinite-dimensional spaces
Four vertex theorem - every convex curve has at least 4 vertices.
Gift wrapping algorithm
Graham scan
Hadwiger conjecture (combinatorial geometry) - any convex body in n-dimensional Euclidean space can be covered by 2n or fewer smaller bodies homothetic with the original body.
Hadwiger's theorem - a theorem that characterizes the valuations on convex bodies in Rn.
Helly's theorem
Hyperplane
Indifference curve
Infimal convolute
Interval (mathematics)
Jarvis march
Jensen's inequality
John ellipsoid
Lagrange multiplier
Legendre transformation
Locally convex topological vector space
Mahler volume
Minkowski's theorem
Mixed volume
Mixture density
Newton polygon
Radon's theorem
Separating axis theorem
Shapley–Folkman lemma
Shephard's problem
Simplex
Simplex method
Subdifferential
Supporting hyperplane
Supporting hyperplane theorem
