Semi-Definite Programming as a Simple Extension to Linear Programming: Convex Optimization with Queueing, Equity and Other Telecom Functionals

In the recent years, the telecommunication field has experienced an explosion of services, with as various leading applications as mobility and the Internet. This revolution has impacted both the nature and the volume of the traffic in nowadays networks. Meanwhile, in an attempt to simplify the management of such networks, the protocols that have been proposed recently aim at unifying the way the traffic is carried. In a sense, both ATM and the IP have tried to be the universal model for transiting all kinds of information. Logically, both of these protocols have integrated mechanisms to optimize the way the traffic is routed. However, the optimization software is still today something to improve. The issue is becoming more challenging as many users can interfere in a network, and the impact of these on the final quality of service, including the delay and the equity among users for instance, is becoming increasingly important as the load is getting bursty. In this paper, we introduce the reader to semi-definite programming, and show how complex and new network functionals can be very naturally implemented using this method. After recalling the basics of underlying mathematics and links to linear programming in Section 2, we show in Section 3 how different network functionals can be described as a SDP program. Finally, in Section 4 we mention other significant improvements of the field of algorithms for telecommunication-oriented problems using SDP.