Foundations of Network Optimization and Games

Terry Lee Friesz, David Bernstein

Research output: Book/ReportBook

4 Citations (Scopus)

Abstract

This is a book about infrastructure networks that are intrinsically nonlinear. The networks considered range from vehicular networks to electric power networks to data networks. The main point of view taken is that of mathematical programming in concert with finite-dimensional variational inequality theory. The principle modeling perspectives are network optimization, the theory of Nash games, and mathematical programming with equilibrium constraints. Computational methods and novel mathematical formulations are emphasized. Among the numerical methods explored are network simplex, gradient projection, fixed-point, gap function, Lagrangian relaxation, Dantzig-Wolfe decomposition, simplicial decomposition, and computational intelligence algorithms. Many solved example problems are included that range from simple to quite challenging. Theoretical analyses of several models and algorithms, to uncover existence, uniqueness and convergence properties, are undertaken. The book is meant for use in advanced undergraduate as well as doctoral courses taught in civil engineering, industrial engineering, systems engineering, and operations research degree programs. At the same time, the book should be a useful resource for industrial and university researchers engaged in the mathematical modeling and numerical analyses of infrastructure networks.

Original languageEnglish (US)
PublisherSpringer Science and Business Media, LLC
Number of pages504
Volume3
ISBN (Electronic)9781489975942
ISBN (Print)9781489975935
DOIs
StatePublished - Nov 1 2015

Fingerprint

Network games
Network optimization
Mathematical programming
Uniqueness
Modeling
Mathematical modeling
Electric power
Industrial engineering
Decomposition
Computational methods
Dantzig-Wolfe decomposition
Resources
Operations research
Systems engineering
Numerical methods
Fixed point
Lagrangian relaxation
Gradient
Undergraduate
Civil engineering

All Science Journal Classification (ASJC) codes

  • Economics, Econometrics and Finance(all)
  • Business, Management and Accounting(all)

Cite this

Friesz, T. L., & Bernstein, D. (2015). Foundations of Network Optimization and Games. Springer Science and Business Media, LLC. https://doi.org/10.1007/978-1-4899-7594-2
Friesz, Terry Lee ; Bernstein, David. / Foundations of Network Optimization and Games. Springer Science and Business Media, LLC, 2015. 504 p.
@book{cea6e94cba734ad3ad7b08290b616899,
title = "Foundations of Network Optimization and Games",
abstract = "This is a book about infrastructure networks that are intrinsically nonlinear. The networks considered range from vehicular networks to electric power networks to data networks. The main point of view taken is that of mathematical programming in concert with finite-dimensional variational inequality theory. The principle modeling perspectives are network optimization, the theory of Nash games, and mathematical programming with equilibrium constraints. Computational methods and novel mathematical formulations are emphasized. Among the numerical methods explored are network simplex, gradient projection, fixed-point, gap function, Lagrangian relaxation, Dantzig-Wolfe decomposition, simplicial decomposition, and computational intelligence algorithms. Many solved example problems are included that range from simple to quite challenging. Theoretical analyses of several models and algorithms, to uncover existence, uniqueness and convergence properties, are undertaken. The book is meant for use in advanced undergraduate as well as doctoral courses taught in civil engineering, industrial engineering, systems engineering, and operations research degree programs. At the same time, the book should be a useful resource for industrial and university researchers engaged in the mathematical modeling and numerical analyses of infrastructure networks.",
author = "Friesz, {Terry Lee} and David Bernstein",
year = "2015",
month = "11",
day = "1",
doi = "10.1007/978-1-4899-7594-2",
language = "English (US)",
isbn = "9781489975935",
volume = "3",
publisher = "Springer Science and Business Media, LLC",

}

Friesz, TL & Bernstein, D 2015, Foundations of Network Optimization and Games. vol. 3, Springer Science and Business Media, LLC. https://doi.org/10.1007/978-1-4899-7594-2

Foundations of Network Optimization and Games. / Friesz, Terry Lee; Bernstein, David.

Springer Science and Business Media, LLC, 2015. 504 p.

Research output: Book/ReportBook

TY - BOOK

T1 - Foundations of Network Optimization and Games

AU - Friesz, Terry Lee

AU - Bernstein, David

PY - 2015/11/1

Y1 - 2015/11/1

N2 - This is a book about infrastructure networks that are intrinsically nonlinear. The networks considered range from vehicular networks to electric power networks to data networks. The main point of view taken is that of mathematical programming in concert with finite-dimensional variational inequality theory. The principle modeling perspectives are network optimization, the theory of Nash games, and mathematical programming with equilibrium constraints. Computational methods and novel mathematical formulations are emphasized. Among the numerical methods explored are network simplex, gradient projection, fixed-point, gap function, Lagrangian relaxation, Dantzig-Wolfe decomposition, simplicial decomposition, and computational intelligence algorithms. Many solved example problems are included that range from simple to quite challenging. Theoretical analyses of several models and algorithms, to uncover existence, uniqueness and convergence properties, are undertaken. The book is meant for use in advanced undergraduate as well as doctoral courses taught in civil engineering, industrial engineering, systems engineering, and operations research degree programs. At the same time, the book should be a useful resource for industrial and university researchers engaged in the mathematical modeling and numerical analyses of infrastructure networks.

AB - This is a book about infrastructure networks that are intrinsically nonlinear. The networks considered range from vehicular networks to electric power networks to data networks. The main point of view taken is that of mathematical programming in concert with finite-dimensional variational inequality theory. The principle modeling perspectives are network optimization, the theory of Nash games, and mathematical programming with equilibrium constraints. Computational methods and novel mathematical formulations are emphasized. Among the numerical methods explored are network simplex, gradient projection, fixed-point, gap function, Lagrangian relaxation, Dantzig-Wolfe decomposition, simplicial decomposition, and computational intelligence algorithms. Many solved example problems are included that range from simple to quite challenging. Theoretical analyses of several models and algorithms, to uncover existence, uniqueness and convergence properties, are undertaken. The book is meant for use in advanced undergraduate as well as doctoral courses taught in civil engineering, industrial engineering, systems engineering, and operations research degree programs. At the same time, the book should be a useful resource for industrial and university researchers engaged in the mathematical modeling and numerical analyses of infrastructure networks.

UR - http://www.scopus.com/inward/record.url?scp=84958616326&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84958616326&partnerID=8YFLogxK

U2 - 10.1007/978-1-4899-7594-2

DO - 10.1007/978-1-4899-7594-2

M3 - Book

AN - SCOPUS:84958616326

SN - 9781489975935

VL - 3

BT - Foundations of Network Optimization and Games

PB - Springer Science and Business Media, LLC

ER -

Friesz TL, Bernstein D. Foundations of Network Optimization and Games. Springer Science and Business Media, LLC, 2015. 504 p. https://doi.org/10.1007/978-1-4899-7594-2