Mathematical Theory of Optimization

  • Ding-Zhu Du
  • Panos M. Pardalos
  • Weili Wu

Part of the Nonconvex Optimization and Its Applications book series (NOIA, volume 56)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Ding-Zhu Du, Panos M. Pardalos, Weili Wu
    Pages 1-21
  3. Ding-Zhu Du, Panos M. Pardalos, Weili Wu
    Pages 23-40
  4. Ding-Zhu Du, Panos M. Pardalos, Weili Wu
    Pages 41-50
  5. Ding-Zhu Du, Panos M. Pardalos, Weili Wu
    Pages 51-63
  6. Ding-Zhu Du, Panos M. Pardalos, Weili Wu
    Pages 65-79
  7. Ding-Zhu Du, Panos M. Pardalos, Weili Wu
    Pages 81-98
  8. Ding-Zhu Du, Panos M. Pardalos, Weili Wu
    Pages 99-123
  9. Ding-Zhu Du, Panos M. Pardalos, Weili Wu
    Pages 125-132
  10. Ding-Zhu Du, Panos M. Pardalos, Weili Wu
    Pages 133-150
  11. Ding-Zhu Du, Panos M. Pardalos, Weili Wu
    Pages 151-166
  12. Ding-Zhu Du, Panos M. Pardalos, Weili Wu
    Pages 167-185
  13. Ding-Zhu Du, Panos M. Pardalos, Weili Wu
    Pages 187-200
  14. Ding-Zhu Du, Panos M. Pardalos, Weili Wu
    Pages 201-213
  15. Ding-Zhu Du, Panos M. Pardalos, Weili Wu
    Pages 215-226
  16. Ding-Zhu Du, Panos M. Pardalos, Weili Wu
    Pages 227-243
  17. Back Matter
    Pages 245-273

About this book

Introduction

Optimization is of central importance in all sciences. Nature inherently seeks optimal solutions. For example, light travels through the "shortest" path and the folded state of a protein corresponds to the structure with the "minimum" potential energy. In combinatorial optimization, there are numerous computationally hard problems arising in real world applications, such as floorplanning in VLSI designs and Steiner trees in communication networks. For these problems, the exact optimal solution is not currently real-time computable. One usually computes an approximate solution with various kinds of heuristics. Recently, many approaches have been developed that link the discrete space of combinatorial optimization to the continuous space of nonlinear optimization through geometric, analytic, and algebraic techniques. Many researchers have found that such approaches lead to very fast and efficient heuristics for solving large problems. Although almost all such heuristics work well in practice there is no solid theoretical analysis, except Karmakar's algorithm for linear programming. With this situation in mind, we decided to teach a seminar on nonlinear optimization with emphasis on its mathematical foundations. This book is the result of that seminar. During the last decades many textbooks and monographs in nonlinear optimization have been published. Why should we write this new one? What is the difference of this book from the others? The motivation for writing this book originated from our efforts to select a textbook for a graduate seminar with focus on the mathematical foundations of optimization.

Keywords

Computer Variable algorithms combinatorial optimization computer science linear optimization nonlinear optimization optimization programming

Editors and affiliations

  • Ding-Zhu Du
    • 1
  • Panos M. Pardalos
    • 2
  • Weili Wu
    • 1
  1. 1.Department of Computer Science and EngineeringUniversity of MinnesotaMinneapolisUSA
  2. 2.Center for Applied Optimization, ISE DepartmentUniversity of FloridaGainesvilleUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4757-5795-8
  • Copyright Information Springer-Verlag US 2001
  • Publisher Name Springer, Boston, MA
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4419-5202-8
  • Online ISBN 978-1-4757-5795-8
  • Series Print ISSN 1571-568X
  • About this book