# Fast Algorithms for Packing Proportional Fairness and its Dual

arXiv: https://arxiv.org/abs/2109.03678 · HTML: https://mlsanity.com/paper/2109.03678/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Sep 2021.

## Built on by (most cited first, 2 of 2)

- [Accelerated Riemannian Optimization: Handling Constraints with a Prox to Bound Geometric Penalties](https://mlsanity.com/paper/2211.14645/) (2022)
- [Learning-Augmented Online Scheduling with Parsimonious Preemption](https://mlsanity.com/paper/2605.23255/) (2026)

## Abstract (arXiv)

The proportional fair resource allocation problem is a major problem studied in flow control of networks, operations research, and economic theory, where it has found numerous applications. This problem, defined as the constrained maximization of sumi log xi, is known as the packing proportional fairness problem when the feasible set is defined by positive linear constraints and x ∈ ℝn≥ 0. In this work, we present a distributed accelerated first-order method for this problem which improves upon previous approaches. We also design an algorithm for the optimization of its dual problem. Both algorithms are width-independent. Finally, we show the latter problem has applications to the volume reduction of bounding simplices in an old linear programming algorithm of (YL82), and we obtain some improvements as a result.