Bregman-Based Inexact Excessive Gap Method for Multiservice Resource Allocation

Abstract

In order to meet the explosive increasing demand of user application data in modern wireless networks, a variety of multiservice resource allocation algorithms have been proposed in the literature. Most of them can be modeled as optimization problems of minimizing a summation function indicated as $\sum_{i=1}^{N}f_{i}(x_{i} ) $ with additive nonlinear coupling inequality constraints. The existing subgradient methods can only achieve a convergence rate of ${\cal O}(1/\sqrt{k} ) $ , which is quite slow for handling big user data generated from modern heterogeneous wireless networks. To develop more efficient multiservice resource allocation algorithms, we consider the regularized Lagrangian function with smoothing accelerated techniques. Specifically, in this paper, we extend the previous research that mainly focuses on linear coupling equality constraints to a challenging scenario with nonlinear coupling inequality constraints. To solve the problem, we propose and analyze a Bregman-based inexact excessive gap (BIEG algorithm, which, by rigorous mathematical proofs, can asymptotically achieve a faster convergence rate of ${\cal O} (1/k) $ . Furthermore, the BIEG method is applied to develop a novel multiservice resource allocation algorithm, namely, BIEG-RA, which combines the accuracy control mechanism with the Bregman projection technique. Numerical results verify its fast convergence rate in heterogeneous wireless networks.