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Opposite of concave . A geometric shape is convex if all its edges point outwards. That is no part of it curves or faces inwards. If a shape is convex, a line segment drawn between any two points on the shape will always lie inside the shape. The figure above is a convex pentagon. No part of it is caved in and any line segment, such as the red one shown, linking two points on it always lies inside the shape. See also Concave definition.
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. Every real-valued linear transformation is convex but not strictly convex, since if f is linear, then This statement also holds if we replace convex by concave. 2  Every real-valued affine function, i.e., each function of the form, is simultaneously convex and concave.