Gradient descent for β-smooth, α-strongly convex

Let $f$ be a β-smooth and α-strongly convex function. If we run GD for $T$ steps (with step size $η = \frac{1}{β}$) we have: $$||\mathbf{x}^{(T)} − \mathbf{x}^*||_2^2 ≤ e^{−T\frac{α}{β}} ||\mathbf{x}^{(0)}−\mathbf{x}^*||_2^2$$

$\kappa = \frac{\beta}{\alpha}$ is called the condition number of $f$

compare: Gradient descent convergence for β-smooth functions, Gradient descent convergence for α-strongly convex functions