Foundations of network optimization and games
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 process of user equilibrium determination. The connection is performed via a mathematical program with equilibrium constraints, which can describe a Stackelberg game played among a network optimizer and the independent users. Generally, it can be stated that the book constitutes a precious guide for researchers and advanced students to the field of network flow problems.
scientific article; zbMATH DE number 6505527