Convex optimization over fixed point sets of quasi-nonexpansive and nonexpansive mappings in utility-based bandwidth allocation problems with operational constraints

Network bandwidth allocation is a central issue in modern communication networks. The main objective of the bandwidth allocation is to allocate an optimal bandwidth for maximizing a predefined utility over the capacity constraints to traffic sources. When a centralized operator, which manages all the bandwidth allocations in the network, has a certain operational policy, the bandwidth allocation reflecting the operational policy should result in the network being more stable and reliable. Accordingly, we need to solve a network bandwidth allocation problem under both capacity constraints and operational constraints. To develop a novel algorithm for solving the problem, we translate the network bandwidth allocation problem into one of minimizing a convex objective function over the intersection of the fixed point sets of certain quasi-nonexpansive and nonexpansive mappings and propose a fixed point optimization algorithm for solving it. We numerically compare the proposed algorithm with the existing algorithm for solving a concrete bandwidth allocation problem and show its effectiveness.