I read this theorem in the textbook Numerical Optimization, but I could not figure out the proof for this theorem.
Suppose $f$ is differentiable and is strongly convex with modulus $m$ and the gradient is Lipschitz with constant $M$. Then,
$[∇f(x) − ∇f(y)] · (x − y) ≥ \frac{Mm}{M + m} ||x - y||^2 + \frac{1}{M + m} ||∇f(x) − ∇f(y)||^2$
How do I prove this theorem?