The iterates of FISTA converge even under inexact computations and stochastic gradients

Saverio Salzo

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arXiv · 2511.12665

The iterates of FISTA converge even under inexact computations and stochastic gradients

Saverio Salzo

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Abstract

Very recently, the papers "Point Convergence of Nesterov's Accelerated Gradient Method: An AI-Assisted Proof" by Jang and Ryu, and "The Iterates of Nesterov's Accelerated Algorithm Converge in the Critical Regimes" by Bot, Fadili, and Nguyen have simultaneously resolved a long-standing open problem concerning Nesterov's accelerated gradient method. These works show that the iterates of the algorithm (known in its composite form as FISTA) indeed converge to an optimal solution. In this work, we extend these results and prove that, in infinite dimensional Hilbert spaces, the iterates of such an algorithm still converge (in the weak sense) even when the proximity operator and the gradient are computed inexactly, with the latter possibly stochastic.

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Saverio Salzo. 2025-11-16. The iterates of FISTA converge even under inexact computations and stochastic gradients. https://arxiv.org/abs/2511.12665

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