Ads
related to: convex function pdf converter freepdf-format.com has been visited by 100K+ users in the past month
Search results
Results from the WOW.Com Content Network
A function (in black) is convex if and only if the region above its graph (in green) is a convex set. A graph of the bivariate convex function x 2 + xy + y 2. Convex vs. Not convex
In 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, the modulus of convexity has the same relationship to the ε-δ definition of uniform convexity as the modulus of continuity does to the ε-δ definition of continuity.
Convex analysis includes not only the study of convex subsets of Euclidean spaces but also the study of convex functions on abstract spaces. 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.
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) of a given element in that set. It is similar to the usual indicator function , and one can freely convert between the two, but the characteristic function as defined below is better ...
This follows from the fact that the logarithm is monotone implying that the superlevel sets of this function are convex. [1] Every concave function that is nonnegative on its domain is log-concave. However, the reverse does not necessarily hold. An example is the Gaussian function f(x) = exp(−x 2 /2) which is log-concave since log f(x) = −x ...
The convexity of a measure μ on n-dimensional Euclidean space R n in the sense above is closely related to the convexity of its probability density function. [2] Indeed, μ is s-convex if and only if there is an absolutely continuous measure ν with probability density function ρ on some R k so that μ is the push-forward on ν under a linear ...
Ads
related to: convex function pdf converter freepdf-format.com has been visited by 100K+ users in the past month