Fast Algorithms for Packing Proportional Fairness and its Dual

David Martínez-Rubio, Francisco Criado, Sebastian Pokutta

Abstract: The proportional fair resource allocation problem is a major problem studied in flow control of networks, operations research, and economic theory, where P it has found numerous applications. This problem, defined as the constrained maximization of $\sum_i \log x_i$ , is known as the packing proportional fairness problem when the feasible set is defined by positive linear constraints and x∈R≥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.