closed 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 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. 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 Fixed-point theorems in infinite-dimensional spaces, generalise the Brouwer fixed-point 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