In the field of mathematics known as convex analysis, the characteristic function of a set is a convex function that indicates the membership (or non-membership)...

mathematical analysis, in particular the subfields of convex analysis and optimization, a proper convex function is an extended real-valued convex function with...

devoted to the study of properties of convex sets and convex functions is called convex analysis. Spaces in which convex sets are defined include the Euclidean...

A and 0 at points of X − A. The characteristic function in convex analysis, closely related to the indicator function of a set: χ A ( x ) := { 0 , x ∈...

a top-level heading. As in complex analysis of functions of one variable, which is the case n = 1, the functions studied are holomorphic or complex analytic...

In probability theory and statistics, the characteristic function of any real-valued random variable completely defines its probability distribution....

("receiver operating characteristic"). It was soon introduced to psychology to account for the perceptual detection of stimuli. ROC analysis has been used in...

are reversed, so that we say the cost game is convex if the characteristic function is submodular. Convex cooperative games have many nice properties:...

the characteristic function in convex analysis, which is defined as if using the reciprocal of the standard definition of the indicator function. A related...

sigmoid function is any mathematical function whose graph has a characteristic S-shaped or sigmoid curve. A common example of a sigmoid function is the...

computational package, the function princomp computes principal component analysis, the function pca computes principal component analysis with standardized variables...

A {\displaystyle A} is an open set. In the field of convex analysis, the characteristic function of a set A ⊂ X {\displaystyle A\subset X} is defined...

In geometry, the convex hull, convex envelope or convex closure of a shape is the smallest convex set that contains it. The convex hull may be defined...

In mathematical analysis, the Dirac delta function (or δ distribution), also known as the unit impulse, is a generalized function on the real numbers...

uniformly convex. Conversely, L ∞ {\displaystyle L^{\infty }} is not uniformly convex. Modulus and characteristic of convexity Uniformly convex function Uniformly...

with replacing a non-convex function with its convex closure, that is the function that has the epigraph that is the closed convex hull of the original...

and faces in more than one way, the Euler characteristic will be the same for these subdivisions. For a convex polyhedron, or more generally any simply...

seminorm is a sublinear function and thus satisfies all properties of the latter. In particular, every norm is a convex function. The concept of unit circle...

(Greek Mathematical Society) 1975. Online Conference on Advances in Convex Analysis and Global Optimization (Honoring the memory of C. Carathéodory) June...

mathematics, in the field of functional analysis, a Minkowski functional (after Hermann Minkowski) or gauge function is a function that recovers a notion of distance...

Brouwer. It states that for any continuous function f {\displaystyle f} mapping a nonempty compact convex set to itself, there is a point x 0 {\displaystyle...

Algebra. Danvers, John Wiley & Sons, 2004. A function f is log-convex if and only if log(f) is a convex function. The base of the logarithm does not matter...

minimum under certain assumptions on the function F {\displaystyle F} (for example, F {\displaystyle F} convex and ∇ F {\displaystyle \nabla F} Lipschitz)...

systems Convex conjugate, the ("dual") lower-semicontinuous convex function resulting from the Legendre–Fenchel transformation of a "primal" function Conjugate...

cumulant-generating function as the natural logarithm of the characteristic function, which is sometimes also called the second characteristic function, H ( t )...

density is a function constant inside a given convex body and vanishing outside; it corresponds to the uniform distribution on the convex body, which explains...

the range of any real-valued, non-atomic vector measure is compact and convex Lyapunov–Malkin theorem, a mathematical theorem detailing nonlinear stability...

mathematics, the modulus of convexity and the characteristic of convexity are measures of "how convex" the unit ball in a Banach space is. In some sense...

complex analysis and probability theory. In contrast with enumerative combinatorics, which uses explicit combinatorial formulae and generating functions to...

2013.03.001. Convex analysis (cf. Werner Fenchel) Convex function Characteristic function (convex analysis) Closed convex function Convex conjugate Epigraph...