convex inequality

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• Convex function — on an interval. A function (in black) is convex if and only i …   Wikipedia

• Convex 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 …   Wikipedia

• Convex 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… …   Wikipedia

• Convex polytope — A 3 dimensional convex polytope A 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.[1] Some authors use the terms convex polytope and convex… …   Wikipedia

• Inequality of arithmetic and geometric means — In mathematics, the inequality of arithmetic and geometric means, or more briefly the AM GM inequality, states that the arithmetic mean of a list of non negative real numbers is greater than or equal to the geometric mean of the same list; and… …   Wikipedia

• Convex metric space — An illustration of a convex metric space. In mathematics, convex metric spaces are, intuitively, metric spaces with the property any segment joining two points in that space has other points in it besides the endpoints. Formally, consider a… …   Wikipedia

• Convex body — In mathematics, a convex body in n dimensional Euclidean space Rn is a compact convex set with non empty interior. A convex body K is called symmetric if it is centrally symmetric with respect to the origin, i.e. a point x lies in K if and only… …   Wikipedia

• Jensen's inequality — In mathematics, Jensen s inequality, named after the Danish mathematician Johan Jensen, relates the value of a convex function of an integral to the integral of the convex function. It was proved by Jensen in 1906 [Jensen, J. Sur les fonctions… …   Wikipedia

• Minkowski's first inequality for convex bodies — In mathematics, Minkowski s first inequality for convex bodies is a geometrical result due to the German mathematician Hermann Minkowski. The inequality is closely related to the Brunn–Minkowski inequality and the isoperimetric inequality.… …   Wikipedia

• Isoperimetric inequality — The isoperimetric inequality is a geometric inequality involving the square of the circumference of a closed curve in the plane and the area of a plane region it encloses, as well as its various generalizations. Isoperimetric literally means… …   Wikipedia

• Linear inequality — In mathematics a linear inequality is an inequality which involves a linear function.Formal definitionsWhen operating in terms of real numbers, linear inequalities are the ones written in the forms: f(x) < b ext{ or }f(x) leq b,where f(x) is a… …   Wikipedia