Foundations of network optimization and games
type: Item
instance of: scholarly article
title: Foundations of network optimization and games
zbMATH Open document ID: 1344.90062
DOI: 10.1007/978-1-4899-7594-2
author: David Bernstein
author: Terry L. Friesz
published in: Complex Networks and Dynamic Systems
publication date: 2015-11-06T00:00:00Z
review text: The book presents an excellent comprehensive introduction to the area of network flow problems, where not only a system optimum is searched, but also the behaviour of competing non-cooperative users is taken into account. The authors start their book with an overview of possible application areas, which include practical problems related to transportation and telecommunication networks and also to specific networks such as the electric power network and water resource network. The rudimentary sequence of chapters from two to six is devoted to solving techniques and the associated theoretical background related to the network problems. This part of the book comprises foundations of nonlinear programming and graph theory and their issues in methods and algorithms for solving linear and nonlinear network problems or the problems which have near-network structure. Most of the treated topics are accompanied by proofs of propositions and numerous solved examples, which demonstrate the particular procedures for obtaining an optimal solution of the given problem. In the next part of the book, the authors enlarge the classical variety of the network problems by introducing a further phenomenon playing role in practical network flow problems. The phenomenon is a set of non-cooperative agents or system users, which follow their own particular interest independently of possible public interests, which are usually expressed by the problem objective of the classical network problems. The behaviour of the agents is modelled as a non-cooperative game and the Nash equilibrium is considered to be a resulting state of the user's behaviour. Chapters seven, eight and nine are devoted to the associated models, relationships and solving tools, where the variational inequality plays a substantial role. Whereas the latter part of book deals with methods for the determination of a user equilibrium, the concluding chapter connects the process of searching for a system optimal solution and the…
reviewed by: Jaroslav Janáček
Mathematics Subject Classification ID: 90C35
Mathematics Subject Classification ID: 90-02
Mathematics Subject Classification ID: 90C90
Mathematics Subject Classification ID: 90C10
Mathematics Subject Classification ID: 91A10
zbMATH DE Number: 6505527
zbMATH Keywords: network flow optimization
zbMATH Keywords: nonlinear objective
zbMATH Keywords: variational inequality
zbMATH Keywords: Nash equilibrium
zbMATH Keywords: Stackelberg game
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/978-1-4899-7594-2
OpenAlex ID: W2335515313
description: scientific article; zbMATH DE number 6505527