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1st Edition

# Optimization for Communications and Networks

By

## Poompat Saengudomlert

ISBN 9781578087242
Published September 22, 2011 by CRC Press
220 Pages 64 B/W Illustrations

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## Book Description

This book provides an introduction to optimization theory and its applications. It is written for senior undergraduate students and first-year graduate students of telecommunication and related fields. Most applications pertain to communication and network problems. The book has practical examples to accompany rigorous discussion so that the reader may develop intuitive understanding on relevant concepts. The materials have been developed from course notes. By attempting to cover convex, linear, and integer optimization for a one-semester course, the author focuses on fundamental concepts and techniques rather than trying to be comprehensive. Infact, the book is written with the main intention to serve as a bridge for students with no prior background in optimization to be able to access more advanced books on the subject later on.

Preface
List of Figures
Introduction
Components of Optimization Problems
Classes of Optimization Problems
Convex Optimization
Convex Sets and Convex Functions
Properties of Convex Optimization
Further Properties of Convex Sets
Dual Problems
Lagrange Multipliers
Primal-Dual Optimality Conditions
Sensitivity Analysis
Notes on Maximization Problems
Numerical Algorithms for Unconstrained Optimization
Numerical Algorithms for Constrained Optimization
Application: Transmit Power Allocation
Application: Minimum Delay Routing
Exercise Problems
Linear Optimization
Illustrative Example
Properties of Linear Optimization Problems
Simplex Algorithm
Duality for Linear Optimization
Application: Minimum Cost Routing 983.6 Application: Maximum Lifetime Routing in a WSN
Exercise Problems
Integer Linear Optimization
Illustrative Examples
Branch-and-Bound
Cutting-Plane Algorithm
Duality for Integer Linear Optimization
Heuristics for Integer Linear Optimization
Application: RWA in a WDM Network
Application: Network Topology Design
Exercise Problems
Appendix A: Reviews of Related Mathematics
Review of Linear Algebra
Review of Analysis
Appendix B: Solutions to Exercise Problems
Appendix C: Octave Commands for Optimization
Minimum Cost Routing
Maximum Lifetime Routing in a WSN
RWA in a WDM Network
Network Topology Design
Bibliography
Index

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## Author(s)

### Biography

Saengudomlert\, Poompat