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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
Proper convex function - a convex function whose effective domain is nonempty and it never attains minus infinity. Concave function - the negative of a convex function. Convex geometry - the branch of geometry studying convex sets, mainly in Euclidean space. Contains three sub-branches: general convexity, polytopes and polyhedra, and discrete ...
Convex geometry is a relatively young mathematical discipline. Although the first known contributions to convex geometry date back to antiquity and can be traced in the works of Euclid and Archimedes, it became an independent branch of mathematics at the turn of the 20th century, mainly due to the works of Hermann Brunn and Hermann Minkowski in dimensions two and three.
Pages in category "Convex geometry" The following 54 pages are in this category, out of 54 total. ... Strictly convex set; Support function; Supporting hyperplane;
A function f is called -convex if for any geodesic with natural parameter , the function () is convex. Convex A subset K of a Riemannian manifold M is called convex if for any two points in K there is a unique shortest path connecting them which lies entirely in K, see also totally convex .
The branch of mathematics 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 spaces, the affine spaces over the real numbers, and certain non-Euclidean geometries. The notion of a convex set in Euclidean spaces can be generalized in ...
Convex function, when the line segment between any two points on the graph of the function lies above or on the graph; Convex conjugate, of a function; Convexity (algebraic geometry), a restrictive technical condition for algebraic varieties originally introduced to analyze Kontsevich moduli spaces
A convex curve (black) forms a connected subset of the boundary of a convex set (blue), and has a supporting line (red) through each of its points. A parabola, a convex curve that is the graph of the convex function () = In geometry, a convex curve is a plane curve that has a supporting line through each of its points.