convex sum
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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
Convex set — A convex set … Wikipedia
Convex hull — The convex hull of the red set is the blue convex set. See also: Convex set and Convex combination In mathematics, the convex hull or convex envelope for a set of points X in a real vector space V is the min … Wikipedia
Convex combination — Given three points x1,x2,x3 in a plane as shown in the figure, the point P is a convex combination of the three points, while Q is not. (Q is however an affine combination of the three poin … 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 — 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… … Wikipedia
Locally convex topological vector space — In functional analysis and related areas of mathematics, locally convex topological vector spaces or locally convex spaces are examples of topological vector spaces (TVS) which generalize normed spaces. They can be defined as topological vector… … Wikipedia
Proper 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… … Wikipedia
Carathéodory's theorem (convex hull) — See also Carathéodory s theorem for other meanings In convex geometry Carathéodory s theorem states that if a point x of R d lies in the convex hull of a set P , there is a subset P prime; of P consisting of d +1 or fewer points such that x lies… … Wikipedia
Absolutely convex set — A set C in a real or complex vector space is said to be absolutely convex if it is convex and balanced. Properties A set C is absolutely convex if and only if for any points x 1, , x 2 in C and any numbers lambda 1, , lambda 2 satisfying |lambda… … 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