Differentiable convex functions II

We finish the proof of the theorem by showing that a monotone gradient implies convexity and prove that convexity of a twice differentiable function is equivalent to the Hessian being positive semidefinite at each point.

[sbanert]

Correction: It must be $d \in \mathcal{H}$ instead of $d \in \mathbb{R}^n$ at the beginning of the second proof.

[fariasmaia]

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