List of convexity topics
https://en.wikipedia.org/wiki/List_of_convexity_topics
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 nonnegative 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 nonlinear 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 R^{d} 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 nonnegative 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 nonempty.
 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 all of whose sublevel sets are closed sets.
 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 subbranches: 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 2dimensional polygon whose interior is a convex set in the Euclidean plane.
 Convex polytope  an ndimensional polytope which is also a convex set in the Euclidean ndimensional space.
 Convex set  a set in Euclidean space in which contains every segment between every two of its points.
 Convexity (finance)  refers to nonlinearities 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 higherorder derivatives of the modeling function. Geometrically, the model is no longer flat but curved, and the degree of curvature is called the convexity.
 Duality (optimization)
 Epigraph (mathematics)  for a function f : Rn→R, the set of points lying on or above its graph
 Extreme point  for a convex set S in a real vector space, a point in S which does not lie in any open line segment joining two points of S.
 Fenchel conjugate
 Fenchel's inequality
 Fixedpoint theorems in infinitedimensional spaces, generalise the Brouwer fixedpoint theorem. They have applications, for example, to the proof of existence theorems for partial differential equations
 Four vertex theorem  every convex curve has at least 4 vertices.
 Gift wrapping algorithm  an algorithm for computing the convex hull of a given set of points
 Graham scan  a method of finding the convex hull of a finite set of points in the plane with time complexity O(n log n)
 Hadwiger conjecture (combinatorial geometry)  any convex body in ndimensional Euclidean space can be covered by 2^{n} or fewer smaller bodies homothetic with the original body.
 Hadwiger's theorem  a theorem that characterizes the valuations on convex bodies in R^{n}.
 Helly's theorem
 Hyperplane  a subspace whose dimension is one less than that of its ambient space
 Indifference curve
 Infimal convolute
 Interval (mathematics)  a set of real numbers with the property that any number that lies between two numbers in the set is also included in the set
 Jarvis march
 Jensen's inequality  relates the value of a convex function of an integral to the integral of the convex function
 John ellipsoid  E(K) associated to a convex body K in ndimensional Euclidean space Rn is the ellipsoid of maximal ndimensional volume contained within K.
 Lagrange multiplier  a strategy for finding the local maxima and minima of a function subject to equality constraints
 Legendre transformation  an involutive transformation on the realvalued convex functions of one real variable
 Locally convex topological vector space  example of topological vector spaces (TVS) that generalize normed spaces
 Mahler volume  a dimensionless quantity that is associated with a centrally symmetric convex body
 Minkowski's theorem  any convex set in ℝn which is symmetric with respect to the origin and with volume greater than 2n d(L) contains a nonzero lattice point
 Mixed volume
 Mixture density
 Newton polygon  a tool for understanding the behaviour of polynomials over local fields
 Radon's theorem  on convex sets, that any set of d + 2 points in Rd can be partitioned into two disjoint sets whose convex hulls intersect
 Separating axis theorem
 Shapley–Folkman lemma  a result in convex geometry with applications in mathematical economics that describes the Minkowski addition of sets in a vector space
 Shephard's problem  a geometrical question

Simplex  a generalization of the notion of a triangle or tetrahedron to arbitrary dimensions
 Simplex method  a popular algorithm for linear programming
 Subdifferential  generalization of the derivative to functions which are not differentiable

Supporting hyperplane  a hyperplane meeting certain conditions
 Supporting hyperplane theorem  that defines a supporting hyperplane