Optimization, Stability, and Chaos Theory : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : :

Any complex system demands that its resources be optimally utilized. The resources of the system have to be optimized for it to work efficiently. Therefore a careful and relevant mathematical model of the system is necessary. The phenomenon of Internet is also like any other complex system. Mathematical prerequisites to build and analyse optimization models of the Internet are outlined in this chapter. The following topics are discussed in this chapter: basics of optimization theory, certain useful inequalities, elements of linear programming, optimization techniques, calculus of variations, stability theory, and chaos theory.