There are certain conditions for convexity of functions. In this post we will look at how these conditions change in case of functionals.

Lipschitz continuity

A differentiable function \(f\) is said to have an L-Lipschitz smooth if its derivatives are Lipschitz continuous with L.

\[\forall x, y \in \mathcal{R}, ||\nabla f(x) - \nabla f(y)|| \leq L||x-y||\]

List of equivalent conditions

Todo add more