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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
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 ...
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.
Download as PDF; Printable version; ... In mathematics, a convex graph may be a convex bipartite graph; a convex ... the graph of a convex function
Download as PDF; Printable version; ... is convex, the sublevel sets of convex functions are convex, ... It is possible to convert a convex program in standard form ...
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 ...
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