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Convex and strictly convex grid drawings of the same graph. In graph drawing, a convex drawing of a planar graph is a drawing that represents the vertices of the graph as points in the Euclidean plane and the edges as straight line segments, in such a way that all of the faces of the drawing (including the outer face) have a convex boundary.
A function f is concave over a convex set if and only if the function −f is a convex function over the set. The sum of two concave functions is itself concave and so is the pointwise minimum of two concave functions, i.e. the set of concave functions on a given domain form a semifield.
A graph of the bivariate convex function x 2 + xy + y 2. Convex vs. Not convex. In mathematics, a real-valued function is called convex if the line segment between any two distinct points on the graph of the function lies above or on the graph between the two points. Equivalently, a function is convex if its epigraph (the set of points on or ...
Convex function - a function in which the line segment between any two points on the graph of the function lies above the graph. Closed convex function - a convex function all of whose sublevel sets are closed sets. Proper convex function - a convex function whose effective domain is nonempty and it never attains minus infinity. Concave ...
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 ...
Given a function: from a set X (the domain) to a set Y (the codomain), the graph of the function is the set [4] = {(, ()):}, which is a subset of the Cartesian product.In the definition of a function in terms of set theory, it is common to identify a function with its graph, although, formally, a function is formed by the triple consisting of its domain, its codomain and its graph.
The convex-hull operation is needed for the set of convex sets to form a lattice, in which the "join" operation is the convex hull of the union of two convex sets = = ( ()). The intersection of any collection of convex sets is itself convex, so the convex subsets of a (real or complex) vector space form a complete lattice .
The second derivative of a function f can be used to determine the concavity of the graph of f. [2] A function whose second derivative is positive is said to be concave up (also referred to as convex), meaning that the tangent line near the point where it touches the function will lie below the graph of the function.