Optimal urban networks via mass transportation / Giuseppe Buttazzo, Aldo Pratelli, Sergio Solimini, ... [et al.]

The monograph is dedicated to a class of models of optimization of transportation networks (urban traffic networks or networks of railroads and highways) in a given geographic area. The book is structured into six chapters. The first one is an introduction to networks and the problems that are studied in this book. The notation and the preliminaries to rigorously set the problem of optimal networks are introduced in the second chapter. In Chapter 3 the problem of finding an optimal network under the additional constraint that the admissible networks are assumed connected is considered. In Chapter 4 the relaxed optimization problem is introduced and it is shown that it always admits a solution. In Chapter 5 the existence of relaxed solutions to network optimization problems, and conditions for the existence of classical solutions are given. The last chapter is dedicated to the analysis of the two-dimensional case. (Zentralblatt)