convex function
1Convex function — on an interval. A function (in black) is convex if and only i …
2Logarithmically convex function — In mathematics, a function f defined on an convex subset of a real vector space and taking positive values is said to be logarithmically convex if log f(x) is a convex function of x.It is easy to see that a logarithmically convex function is a… …
3Proper convex function — In mathematics, a proper convex function is a convex function f taking values in the extended real number line such that:f(x) < +inftyfor at least one x and :f(x) > inftyfor every x . This definition takes account of the fact that the extended… …
4Schur-convex function — In mathematics, a Schur convex function, also known as S convex, isotonic function and order preserving function is a function f: mathbb{R}^d ightarrow mathbb{R}, for which if forall x,yin mathbb{R}^d where x is majorized by y, then f(x)le f(y).… …
5Closed convex function — In mathematics, a convex function is called closed if its epigraph is a closed set. Properties A closed convex function f is the pointwise supremum of the collection of all affine functions h such that h≤f. References Rockafellar, R. Tyrell,… …
6Convex optimization — Convex minimization, a subfield of optimization, studies the problem of minimizing convex functions over convex sets. Given a real vector space X together with a convex, real valued function defined on a convex subset of X, the problem is to find …
7Convex conjugate — In mathematics, convex conjugation is a generalization of the Legendre transformation. It is also known as Legendre–Fenchel transformation or Fenchel transformation (after Adrien Marie Legendre and Werner Fenchel). Contents 1 Definition 2… …
8Convex set — A convex set …
9Convex preferences — In 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 . The concept roughly corresponds to the law of diminishing… …
10Convex — 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… …
