A DC Programming Approach for Solving Multicast Network Design Problems via the Nesterov Smoothing Technique

TL;DR

This paper introduces a novel continuous optimization approach using Nesterov smoothing and DCA algorithms to solve discrete multicast network design problems, demonstrating effectiveness through numerical experiments.

Contribution

It reformulates discrete multicast network design problems as continuous problems and applies Nesterov smoothing with DCA algorithms, a novel approach in this context.

Findings

Effective continuous reformulation of discrete problems

Successful application of Nesterov smoothing technique

Numerical results validate the approach

Abstract

This paper continues our effort initiated in [9] to study Multicast Communication Networks, modeled as bilevel hierarchical clustering problems, by using mathematical optimization techniques. Given a finite number of nodes, we consider two different models of multicast networks by identifying a certain number of nodes as cluster centers, and at the same time, locating a particular node that serves as a total center so as to minimize the total transportation cost through the network. The fact that the cluster centers and the total center have to be among the given nodes makes this problem a discrete optimization problem. Our approach is to reformulate the discrete problem as a continuous one and to apply Nesterov smoothing approximation technique on the Minkowski gauges that are used as distance measures. This approach enables us to propose two implementable DCA-based algorithms for solving the problems. Numerical results and practical applications are provided to illustrate our approach.