Distributed iterative aggregation algorithms for box-constrained minimization problems and optimal routing in data networks

A new gradient projection algorithm using iterative aggregation and disaggregation is proposed and analyzed for box-constrained minimization problems. In a distributed computation model, the algorithm is shown to converge. As an important application, the authors also show how the algorithm is applied to optimal routing in a large interconnected data communication network. The aggregation/disaggregation method proposed results in a multilevel hierarchical clustering of a large network, which naturally fits the hierarchical topological structure of large networks. An implementation of the algorithm for a 52-node network shows that the serial version of the algorithm has a savings of 35 percent of the computational time as compared to a path-formulated gradient projection code developed by Bertsekas, Gendron, and Tsai, which is among the fastest existing programs for path-formulated optimal routing.