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In convex analysis, a non-negative function f : R n → R + is logarithmically concave (or log-concave for short) if its domain is a convex set, and if it satisfies the inequality (+ ()) () for all x,y ∈ dom f and 0 < θ < 1.
Convex functions are related to convex sets. Specifically, the function is convex if and only if its epigraph. A function (in black) is convex if and only if its epigraph, which is the region above its graph (in green), is a convex set. A graph of the bivariate convex function + +.
When a some complete Reinhardt domain to be the domain of convergence of a power series, an additional condition is required, which is called logarithmically-convex. A Reinhardt domain D is called logarithmically convex if the image () of the set
In convex analysis, a branch of mathematics, the effective domain extends of the domain of a function defined for functions that take values in the extended real number line [,] = {}. In convex analysis and variational analysis , a point at which some given extended real -valued function is minimized is typically sought, where such a point is ...
In complex geometry and analysis, the notion of convexity and its generalizations play an important role in understanding function behavior. Examples of classes of functions with a rich structure are, in addition to the convex functions, the subharmonic functions and the plurisubharmonic functions.
Download as PDF; Printable version; In other projects ... In mathematics, a convex graph may be a convex bipartite graph; a convex plane graph; the graph of a convex ...
The convex hull of a simple polygon is divided by the polygon into pieces, one of which is the polygon itself and the rest are pockets bounded by a piece of the polygon boundary and a single hull edge. Although many algorithms have been published for the problem of constructing the convex hull of a simple polygon, nearly half of them are ...