convex functional
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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 geometry — is the branch of geometry studying convex sets, mainly in Euclidean space. Convex sets occur naturally in many areas of mathematics: computational geometry, convex analysis, discrete geometry, functional analysis, geometry of numbers, integral… … Wikipedia
Convex set — A convex set … 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
Functional derivative — In mathematics and theoretical physics, the functional derivative is a generalization of the directional derivative. The difference is that the latter differentiates in the direction of a vector, while the former differentiates in the direction… … 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
Minkowski functional — In functional analysis, given a linear space X, a Minkowski functional is a device that uses the linear structure to introduce a topology on X. Contents 1 Motivation 1.1 Example 1 1.2 Example 2 2 … Wikipedia
Orthogonal convex hull — The orthogonal convex hull of a point set In Euclidean geometry, a set is defined to be orthogonally convex if, for every line L that is parallel to one of the axes of the Cartesian coordinate system, the intersection of K with L is empty, a… … Wikipedia
List of functional analysis topics — This is a list of functional analysis topics, by Wikipedia page. Contents 1 Hilbert space 2 Functional analysis, classic results 3 Operator theory 4 Banach space examples … Wikipedia
State (functional analysis) — In functional analysis, a state on a C* algebra is a positive linear functional of norm 1. The set of states of a C* algebra A , sometimes denoted by S ( A ), is always a convex set. The extremal points of S ( A ) are called pure states. If A has … Wikipedia
Tonelli's theorem (functional analysis) — In mathematics, Tonelli s theorem in functional analysis is a fundamental result on the weak lower semicontinuity of nonlinear functionals on L p spaces. As such, it has major implications for functional analysis and the calculus of variations.… … Wikipedia