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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.
Printable version; Page information ... Convex curve through 13 points of the ... Thicker lines and bigger circles to work better at smaller image sizes: 21:10, 14 ...
Print/export Download as PDF; Printable version; In other projects ... Appearance. move to sidebar hide. In mathematics, a convex graph may be a convex bipartite ...
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.
English: The four types of intersection of a line with a convex curve, here a regular pentagon. The intersections of the four blue lines with the curve, shown in red, are (from top to bottom) the empty set, a single point, two points, and an interval.
A strictly convex function is a function that the straight line between any pair of points on the curve is above the curve except for the intersection points between the straight line and the curve. An example of a function which is convex but not strictly convex is f ( x , y ) = x 2 + y {\displaystyle f(x,y)=x^{2}+y} .
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.