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Additional
convex function
English Wikipedia - The Free Encyclopedia
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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
and the
exponential function
for any real number
x
.
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