2021/09/08 by Criado, Francisco, Martínez-Rubio, David, Pokutta, Sebastian
#FOS: Mathematics #Optimization and Control (math.OC)
paper · doi:10.48550/arxiv.2109.03678
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 ∑i 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.