Handbook of Optimization in Telecommunications M.G.C. Resende and P.M. Pardalos (Editors) Springer Science + Business Media, 2006.
Chapter 2
Nonlinear programming in telecommunications
A. Migdalas
Abstract
Telecommunications have always been the subject of application for advanced mathematical techniques. In this chapter, we review classical nonlinear programming approaches to modeling and solving certain problems in telecommunications. We emphasize the common aspects of telecommunications and road networks, and indicate that several lessons are to be learned from the field of transportation science, where game theoretic and equilibrium approaches have been studied for more than forty years. Several research directions are also stated.
Keywords: Nonlinear optimization, Frank-Wolfe-like algorithms, simplicial decomposition, team games, routing, equilibrium flows, capacity assignment, network design, bilevel programming, Nash equilibrium,Wardrop's principle, Stackelberg game.