Optimization for Communications and Networks

220 Pages·2011·20.074 MB·\220

by  Poompat Saengudomlert (Author)

Optimization for
Communications and
Networks
TThhiiss ppaaggee iinntteennttiioonnaallllyy lleefftt bbllaannkk
Optimization for
Communications and
Networks
Poompat Saengudomlert
School of Engineering and Technology
Asian Institute of Technology, Thailand
CRC Press 6S0u0ite0 3B0ro0k,e Bno cSao uRnadto Pna, rFkwL a3y3, 4N8W7 Science Publishers
@) Taylor & Francis Croup 270 Madison Avenue
V^ ^ an informa business New York, NY 10016 Jersey, British Isles
www.crcpress.com 2 Park Square, Milton Park % Enfield, New Hampshire
Abingdon, Oxon OX14 4RN, UK
CRC Press
Taylor & Francis Group
6000 Broken Sound Parkway NW, Suite 300
Boca Raton, FL 33487-2742
© 2011 by Taylor & Francis Group, LLC
CRC Press is an imprint of Taylor & Francis Group, an Informa business
No claim to original U.S. Government works
Version Date: 20111025
International Standard Book Number-13: 978-1-4398-7656-5 (eBook - PDF)
This book contains information obtained from authentic and highly regarded sources. Reasonable
efforts have been made to publish reliable data and information, but the author and publisher cannot
assume responsibility for the validity of all materials or the consequences of their use. The authors and
publishers have attempted to trace the copyright holders of all material reproduced in this publication
and apologize to copyright holders if permission to publish in this form has not been obtained. If any
copyright material has not been acknowledged please write and let us know so we may rectify in any
future reprint.
Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced,
transmitted, or utilized in any form by any electronic, mechanical, or other means, now known or
hereafter invented, including photocopying, microfilming, and recording, or in any information stor-
age or retrieval system, without written permission from the publishers.
For permission to photocopy or use material electronically from this work, please access www.copy-
right.com (http://www.copyright.com/) or contact the Copyright Clearance Center, Inc. (CCC), 222
Rosewood Drive, Danvers, MA 01923, 978-750-8400. CCC is a not-for-profit organization that pro-
vides licenses and registration for a variety of users. For organizations that have been granted a pho-
tocopy license by the CCC, a separate system of payment has been arranged.
Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are
used only for identification and explanation without intent to infringe.
Visit the Taylor & Francis Web site at
http://www.taylorandfrancis.com
and the CRC Press Web site at
http://www.crcpress.com
To my parents
Natee
and
Supreeya Saengudomlert
TThhiiss ppaaggee iinntteennttiioonnaallllyy lleefftt bbllaannkk
Preface
The book provides an introduction to optimization theory and its
applications. It is written for senior undergraduate students and first-year
graduate students of related fields. Presented example applications are for
communication and network problems.
Optimization theory involves a great deal of mathematics. The book
has work 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 book
focuses on fundamental concepts and techniques rather than trying to be
comprehensive. In fact, 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.
Each main chapter starts with theoretical discussion to be followed
by example applications to practical engineering problems. Exercise
problems are provided at the end of each chapter, with detailed solutions
given in the appendix. Thus, an interested reader can use the book as a
self-study guide. Specific computer programs are also given for examples
that require the use of an optimization software tool. However, since such
tools are fast evolving, there is no attempt to explain them in specific
details besides giving explicit examples.
I am thankful to all my teachers at Assumption College, Bangkok,
Thailand; Triam Udom Suksa School, Bangkok, Thailand; Deerfield
Academy, Deerfield, MA, USA; Princeton University, Princeton, NJ,
USA; and Massachusetts Institute of Technology, Cambridge, MA, USA
for the knowledge as well as the inspiration. I would also like to thank
students who provided valuable feedback.
Poompat Saengudomlert
Asian Institute of Technology
TThhiiss ppaaggee iinntteennttiioonnaallllyy lleefftt bbllaannkk
Contents
Preface vii
List of Figures xi
1. Introduction 1
1.1 Components of Optimization Problems 2
1.2 Classes of Optimization Problems 3
2. Convex Optimization 5
2.1 Convex Sets and Convex Functions 5
2.2 Properties of Convex Optimization 9
2.3 Further Properties of Convex Sets 12
2.4 Dual Problems 16
2.5 Lagrange Multipliers 18
2.6 Primal-Dual Optimality Conditions 23
2.7 Sensitivity Analysis 25
2.8 Notes on Maximization Problems 29
2.9 Numerical Algorithms for Unconstrained Optimization 30
2.10 Numerical Algorithms for Constrained Optimization 35
2.11 Application: Transmit Power Allocation 46
2.12 Application: Minimum Delay Routing 49
2.13 Exercise Problems 56
3. Linear Optimization 67
3.1 Illustrative Example 67
3.2 Properties of Linear Optimization Problems 71
3.3 Simplex Algorithm 79
3.4 Duality for Linear Optimization 92
3.5 Application: Minimum Cost Routing 98