Gradient descent with arbitrary predetermined nonnegative step size schedules has worst-case last-iterate convergence rate at least Omega(T^{-p}) for every p > sqrt(2+sqrt(3)) approximately 1.9319.
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A lower bound for stepsize-based acceleration of gradient descent
Gradient descent with arbitrary predetermined nonnegative step size schedules has worst-case last-iterate convergence rate at least Omega(T^{-p}) for every p > sqrt(2+sqrt(3)) approximately 1.9319.