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Non-convex is also referred to as concave. Convex and non-convex both define the types of curvature. Convex defines the curvature that extends outwards or bulges out. On the other hand, non-convex defines a curvature that extends or bends inward. Thus, the extension of the curve is used to differentiate between the two forms. Convex and non-convex are often used as adjectives to define the entities associated with the shape or curve defined by them.
A function f (x) is concave over a convex set if and only if the function â f (x) is a convex function over the set. A differentiable function f is concave on an interval if its derivative function f â² is monotonically decreasing on that interval: a concave function has a decreasing slope. Any affine function is both (non-strictly) concave and convex. 2  The sine function is concave on the interval. 3  The function, where is the determinant of a nonnegative-definite matrix B, is concave. 4  Practical example: rays bending in computation of radiowave attenuation in the atmosphere.