# Scaled, inexact and adaptive generalized FISTA for strongly convex optimization

arXiv: https://arxiv.org/abs/2101.03915 · HTML: https://mlsanity.com/paper/2101.03915/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Jan 2021.

## Built on by (most cited first, 4 of 4)

- [Deep Equilibrium models for Poisson Imaging Inverse problems via Mirror Descent](https://mlsanity.com/paper/2507.11461/) (2025)
- [DualFL: A Duality-based Federated Learning Algorithm with Communication Acceleration in the General Convex Regime](https://mlsanity.com/paper/2305.10294/) (2023)
- [Adaptive Backtracking Line Search](https://mlsanity.com/paper/2408.13150/) (2024)
- [Self-Tuning Regularization for Image Scanning Microscopy](https://mlsanity.com/paper/2605.31426/) (2026)

## Abstract (arXiv)

We consider a variable metric and inexact version of the FISTA-type algorithm considered in (Chambolle, Pock, 2016, Calatroni, Chambolle, 2019) for the minimization of the sum of two (possibly strongly) convex functions. The proposed algorithm is combined with an adaptive (non-monotone) backtracking strategy, which allows for the adjustment of the algorithmic step-size along the iterations in order to improve the convergence speed. We prove a linear convergence result for the function values, which depends on both the strong convexity moduli of the two functions and the upper and lower bounds on the spectrum of the variable metric operators. We validate the proposed algorithm, named Scaled Adaptive GEneralized FISTA (SAGE-FISTA), on exemplar image denoising and deblurring problems where edge-preserving Total Variation (TV) regularization is combined with Kullback-Leibler-type fidelity terms, as it is common in applications where signal-dependent Poisson noise is assumed in the data.