Convex function

A function (in black) is convex if and only if the region above its graph (in green) is a convex set.

In mathematics, a real-valued function defined on an interval is called convex (or convex downward or concave upward) if the line segment between any two points on the graph of the function lies above or on the graph, in a Euclidean space (or more generally a vector space) of at least two dimensions. Equivalently, a function is convex if its epigraph (the set of points on or above the graph of the function) is a convex set. Well-known examples of convex functions are the quadratic function $x^2$ and the exponential function $e^x$ for any real number x.

单词	Strictly convex
释义	Strictly convex 英语百科 Convex function In mathematics, a real-valued function defined on an interval is called convex (or convex downward or concave upward) if the line segment between any two points on the graph of the function lies above or on the graph, in a Euclidean space (or more generally a vector space) of at least two dimensions. Equivalently, a function is convex if its epigraph (the set of points on or above the graph of the function) is a convex set. Well-known examples of convex functions are the quadratic function $x^2$ and the exponential function $e^x$ for any real number x.
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Strictly convex

Convex function