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2023

Exact convergence rate of the last iterate in subgradient methods

Zamani, Moslem, Glineur, François

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We study the convergence of the last iterate in subgradient methods applied to the minimization of a nonsmooth convex function with bounded subgradients.

We first introduce a proof technique that generalizes the standard analysis of subgradient methods.
It is based on tracking the distance between the current iterate and a different reference point at each iteration.
Using this technique, we obtain the exact worst-case convergence rate for the objective accuracy of the last iterate of the projected subgradient method with either constant step sizes or constant step lengths.

Exact convergence rate of the last iterate in subgradient methods · Around

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Y. Nesterov
2003
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S. Boyd, L. Xiao, and A. Mutapcic
2005
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O. Shamir
2012
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