Lipschitz gradient

A differentiable function has a $\beta$-Lipschitz gradient when

A differentiable function with an $L$-Lipschitz gradient obeys $f(v)\le f(u)+⟨\nabla f(u),v-u⟩+(L/2)\Vert v-u{\Vert }^2$. Integrate the gradient along the line segment and bound the deviation from its initial value. The lemma does not require convexity.