A Proof of Exact Convergence Rate of Gradient Descent. Part I. Performance Criterion $\mathrm{\parallel }\mathrm{\nabla }f(x_N){\mathrm{\parallel }}^2\mathrm{/}(f(x_0)-f_{\ast })$

We prove the exact worst-case convergence rate of gradient descent for smooth strongly convex optimization, with respect to the performance criterion $\mathrm{\parallel }\mathrm{\nabla }f(x_N){\mathrm{\parallel }}^2\mathrm{/}(f(x_0)-f_{\ast })$. The proof differs from the previous one by Rotaru \emph{et al.} [RGP24], and is based on the performance estimation methodology [DT14].