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Linear and Nonlinear Optimization

  • Richard W. Cottle
  • Mukund N. Thapa

Part of the International Series in Operations Research & Management Science book series (ISOR, volume 253)

Table of contents

  1. Front Matter
    Pages i-xxxi
  2. Richard W. Cottle, Mukund N. Thapa
    Pages 1-28
  3. Richard W. Cottle, Mukund N. Thapa
    Pages 29-60
  4. Richard W. Cottle, Mukund N. Thapa
    Pages 61-84
  5. Richard W. Cottle, Mukund N. Thapa
    Pages 85-116
  6. Richard W. Cottle, Mukund N. Thapa
    Pages 117-138
  7. Richard W. Cottle, Mukund N. Thapa
    Pages 139-184
  8. Richard W. Cottle, Mukund N. Thapa
    Pages 185-232
  9. Richard W. Cottle, Mukund N. Thapa
    Pages 233-270
  10. Richard W. Cottle, Mukund N. Thapa
    Pages 271-316
  11. Richard W. Cottle, Mukund N. Thapa
    Pages 317-368
  12. Richard W. Cottle, Mukund N. Thapa
    Pages 369-418
  13. Richard W. Cottle, Mukund N. Thapa
    Pages 419-468
  14. Richard W. Cottle, Mukund N. Thapa
    Pages 469-516
  15. Richard W. Cottle, Mukund N. Thapa
    Pages 517-536
  16. Back Matter
    Pages 537-614

About this book

Introduction

​This textbook on Linear and Nonlinear Optimization is intended for graduate and advanced undergraduate students in operations research and related fields. It is both literate and mathematically strong, yet requires no prior course in optimization. As suggested by its title, the book is divided into two parts covering in their individual chapters LP Models and Applications; Linear Equations and Inequalities; The Simplex Algorithm; Simplex Algorithm Continued; Duality and the Dual Simplex Algorithm; Postoptimality Analyses; Computational Considerations; Nonlinear (NLP) Models and Applications; Unconstrained Optimization; Descent Methods; Optimality Conditions; Problems with Linear Constraints; Problems with Nonlinear Constraints; Interior-Point Methods; and an Appendix covering Mathematical Concepts. Each chapter ends with a set of exercises.

The book is based on lecture notes the authors have used in numerous optimization courses the authors have taught at Stanford University.  It emphasizes modeling and numerical algorithms for optimization with continuous (not integer) variables. The discussion presents the underlying theory without always focusing on formal mathematical proofs (which can be found in cited references). Another feature of this book is its inclusion of cultural and historical matters, most often appearing among the footnotes.


"This book is a real gem. The authors do a masterful job of rigorously presenting all of the relevant theory clearly and concisely while managing to avoid unnecessary tedious mathematical details.  This is an ideal book for teaching a one or two semester masters-level course in optimization – it broadly covers linear and nonlinear programming effectively balancing modeling, algorithmic theory, computation, implementation, illuminating historical facts, and numerous interesting examples and exercises. Due to the clarity of the exposition, this book also serves as a valuable reference for self-study."


Professor Ilan Adler,
IEOR Department,
UC Berkeley


"A carefully crafted introduction to the main elements and applications of mathematical optimization. This volume presents the essential concepts of linear and nonlinear programming in an accessible format filled with anecdotes, examples, and exercises that bring the topic to life. The authors plumb their decades of experience in optimization to provide an enriching layer of historical context. Suitable for advanced undergraduates and masters students in management science, operations research, and related fields."

Michael P. Friedlander,
IBM Professor of Computer Science,
Professor of Mathematics,
University of British Columbia

Keywords

Operations Research Mathematical Programming Optimization Models Linear Programming Nonlinear Programming

Authors and affiliations

  • Richard W. Cottle
    • 1
  • Mukund N. Thapa
    • 2
  1. 1.Stanford UniversityStanfordUSA
  2. 2.Optical Fusion, Inc.Palo AltoUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4939-7055-1
  • Copyright Information Springer Science+Business Media LLC 2017
  • Publisher Name Springer, New York, NY
  • eBook Packages Business and Management
  • Print ISBN 978-1-4939-7053-7
  • Online ISBN 978-1-4939-7055-1
  • Series Print ISSN 0884-8289
  • Series Online ISSN 2214-7934
  • Buy this book on publisher's site