Using z-transforms and Tauberian theory, this paper derives sharp asymptotic rates, such as 1/k^omega for gradient descent and 1/k^{min(2omega, omega+1)} for Nesterov acceleration, for quadratic optimization in infinite dimensions.
Non-asymptotic analysis of stochastic approximation algorithms for machine learning
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On the Effectiveness of the z-Transform Method in Quadratic Optimization
Using z-transforms and Tauberian theory, this paper derives sharp asymptotic rates, such as 1/k^omega for gradient descent and 1/k^{min(2omega, omega+1)} for Nesterov acceleration, for quadratic optimization in infinite dimensions.