2019/09/29 by Anastasiya Ivanova, Ivanova, Anastasiya, Dmitry Pasechnyuk +7
Computer Science · Engineering · #68M10 #90B18 #90C25 #90C30 #C.2.1 #C.2.4 #Complexity and Algorithms in Graphs #FOS: Mathematics #G.1.6 #Optimization and Control (math.OC) #Sparse and Compressive Sensing Techniques #Stochastic Gradient Optimization Techniques
paper · pdf · doi:10.48550/arxiv.1909.13321
openalex publication_date 2019/09/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we consider the resource allocation problem in a network with a large number of connections which are used by a huge number of users. The resource allocation problem under discussion is a maximization problem with linear inequality constraints. To solve this problem we construct the dual problem and propose to use the following numerical optimization methods for the dual: a fast gradient method, a stochastic projected subgradient method, an ellipsoid method, and a random gradient extrapolation method. A special focus is made on the primal-dual analysis of these methods. For each method we estimate the convergence rate. We also provide some modifications of these methods in the setup of distributed computations, taking into account their application to networks.