Table of Contents
9 relations: Continuous linear operator, Convex analysis, Convex set, Dual space, Locally convex topological vector space, Mathematical optimization, Support function, Supporting hyperplane, Topological space.
Continuous linear operator
In functional analysis and related areas of mathematics, a continuous linear operator or continuous linear mapping is a continuous linear transformation between topological vector spaces. Supporting functional and continuous linear operator are functional analysis.
See Supporting functional and Continuous linear operator
Convex analysis
Convex analysis is the branch of mathematics devoted to the study of properties of convex functions and convex sets, often with applications in convex minimization, a subdomain of optimization theory.
See Supporting functional and Convex analysis
Convex set
In geometry, a subset of a Euclidean space, or more generally an affine space over the reals, is convex if, given any two points in the subset, the subset contains the whole line segment that joins them.
See Supporting functional and Convex set
Dual space
In mathematics, any vector space V has a corresponding dual vector space (or just dual space for short) consisting of all linear forms on V, together with the vector space structure of pointwise addition and scalar multiplication by constants. Supporting functional and dual space are Duality theories and functional analysis.
See Supporting functional and Dual space
Locally convex topological vector space
In functional analysis and related areas of mathematics, locally convex topological vector spaces (LCTVS) or locally convex spaces are examples of topological vector spaces (TVS) that generalize normed spaces. Supporting functional and locally convex topological vector space are functional analysis.
See Supporting functional and Locally convex topological vector space
Mathematical optimization
Mathematical optimization (alternatively spelled optimisation) or mathematical programming is the selection of a best element, with regard to some criteria, from some set of available alternatives.
See Supporting functional and Mathematical optimization
Support function
In mathematics, the support function hA of a non-empty closed convex set A in \mathbb^n describes the (signed) distances of supporting hyperplanes of A from the origin. Supporting functional and support function are Types of functions.
See Supporting functional and Support function
Supporting hyperplane
In geometry, a supporting hyperplane of a set S in Euclidean space \mathbb R^n is a hyperplane that has both of the following two properties. Supporting functional and supporting hyperplane are Duality theories and functional analysis.
See Supporting functional and Supporting hyperplane
Topological space
In mathematics, a topological space is, roughly speaking, a geometrical space in which closeness is defined but cannot necessarily be measured by a numeric distance.
See Supporting functional and Topological space