# A globally convergent fast iterative shrinkage-thresholding algorithm with a new momentum factor for single and multi-objective convex optimization

arXiv: https://arxiv.org/abs/2205.05262 · HTML: https://mlsanity.com/paper/2205.05262/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 41 references that are in the map.
- First posted on arXiv 11 May 2022.

## Builds on (most cited first, 10 of 10)

- [Multi-Task Learning as Multi-Objective Optimization](https://mlsanity.com/paper/1810.04650/) (2018)
- [Linear Convergence of Gradient and Proximal-Gradient Methods Under the Polyak-Lojasiewicz Condition](https://mlsanity.com/paper/1608.04636/) (2016)
- [Pareto Multi-Task Learning](https://mlsanity.com/paper/1912.12854/) (2019)
- [A Differential Equation for Modeling Nesterov's Accelerated Gradient Method: Theory and Insights](https://mlsanity.com/paper/1503.01243/) (2015)
- [Efficient Multi-objective Neural Architecture Search via Lamarckian Evolution](https://mlsanity.com/paper/1804.09081/) (2018)
- [DPP-Net: Device-aware Progressive Search for Pareto-optimal Neural Architectures](https://mlsanity.com/paper/1806.08198/) (2018)
- [The rate of convergence of Nesterov's accelerated forward-backward method is actually faster than 1/k2](https://mlsanity.com/paper/1510.08740/) (2015)
- [Convergence rates analysis of a multiobjective proximal gradient method](https://mlsanity.com/paper/2010.08217/) (2020)
- [An accelerated proximal gradient method for multiobjective optimization](https://mlsanity.com/paper/2202.10994/) (2022)
- [New merit functions for multiobjective optimization and their properties](https://mlsanity.com/paper/2010.09333/) (2020)

## Built on by (most cited first, 1 of 1)

- [Fairness-Aware Estimation of Graphical Models](https://mlsanity.com/paper/2408.17396/) (2024)

## Abstract (arXiv)

Convex-composite optimization, which minimizes an objective function represented by the sum of a differentiable function and a convex one, is widely used in machine learning and signal/image processing. Fast Iterative Shrinkage Thresholding Algorithm (FISTA) is a typical method for solving this problem and has a global convergence rate of O(1 / k2). Recently, this has been extended to multi-objective optimization, together with the proof of the O(1 / k2) global convergence rate. However, its momentum factor is classical, and the convergence of its iterates has not been proven. In this work, introducing some additional hyperparameters (a, b), we propose another accelerated proximal gradient method with a general momentum factor, which is new even for the single-objective cases. We show that our proposed method also has a global convergence rate of O(1/k2) for any (a,b), and further that the generated sequence of iterates converges to a weak Pareto solution when a is positive, an essential property for the finite-time manifold identification. Moreover, we report numerical results with various (a,b), showing that some of these choices give better results than the classical momentum factors.