by Dimitri P. Bertsekas
Publication: MAY 1998, 608 pages, hardcover
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An insightful, comprehensive, and up-to-date treatment of linear, nonlinear, and discrete/combinatorial network optimization problems, their applications, and their analytical and algorithmic methodology.
It covers extensively theory, algorithms, and applications, and it aims to bridge the gap between linear and nonlinear network optimization on one hand, and integer/combinatorial network optimization on the other. It complements several of our books: Convex Optimization Theory (Athena Scientific, 2009), Convex Optimization Algorithms (Athena Scientific, 2015), Introduction to Linear Optimization (Athena Scientific, 1997), Nonlinear Programming (Athena Scientific, 1999), as well as our other book on the subject of network optimization Network Flows and Monotropic Optimization (Athena Scientific, 1998).
"This beautifully written book provides an introductory treatment of linear,
nonlinear, and discrete network optimization problems...
The textbook is addressed not only to students of optimization but to all scientists
in numerous disciplines who need network optimization methods to model and solve
problems. This book is an engaging read and it is highly recommended either as a
textbook or as a reference on network optimization."
Among its special features, the book:
provides a comprehensive account of the principal algorithms for linear network flow problems, including simplex, dual ascent, and auction algorithms
describes the application of network algorithms in many practical contexts, with special emphasis on data communication networks
develops in detail the computational complexity analysis of the main linear network optimization algorithms
covers extensively the main algorithms for specialized network problems, such as shortest path, max-flow, assignment, and traveling salesman
describes the main models for discrete network optimization problems, such as constrained shortest path, traveling salesman, vehicle routing, multidimensional assignment, facility location, spanning tree construction, etc
describes the main algorithmic approaches for integer-constrained network problems, such as branch-and-bound, Lagrangian relaxation and subgradient optimization, genetic algorithms, tabu search, simulated annealing, and rollout algorithms
develops the main methods for nonlinear network problems, such as convex separable and multicommodity flow problems arising in communication, transportation, and manufacturing contexts
discusses extensively auction algorithms, based on the author's original research on the subject
contains many examples, practical applications, illustrations, and exercises
contains much new material not found in any other textbook
Dimitri P. Bertsekas is Fulton Professor of Computational Decision Making at the Arizona State University, McAfee Professor of Engineering at the Massachusetts Institute of Technology, and a member of the prestigious United States National Academy of Engineering. He is the recipient of the 2001 A. R. Raggazini ACC education award and the 2009 INFORMS expository writing award. He has also received 2014 ACC Richard E. Bellman Control Heritage Award for "contributions to the foundations of deterministic and stochastic optimization-based methods in systems and control," the 2014 Khachiyan Prize for Life-Time Accomplishments in Optimization, the SIAM/MOS 2015 George B. Dantzig Prize, and the 2022 IEEE Control Systems Award. Together with his coauthor John Tsitsiklis, he was awarded the 2018 INFORMS John von Neumann Theory Prize, for the contributions of the research monographs "Parallel and Distributed Computation" and "Neuro-Dynamic Programming".