Advertisement

Neural Networks in Optimization

  • Xiang-Sun Zhang

Part of the Nonconvex Optimization and Its Applications book series (NOIA, volume 46)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Fundamental Concepts and Models of Optimization

    1. Front Matter
      Pages 1-1
    2. Xiang-Sun Zhang
      Pages 3-29
    3. Xiang-Sun Zhang
      Pages 31-51
  3. Basic Artificial Neural Network Models

    1. Front Matter
      Pages 81-81
    2. Xiang-Sun Zhang
      Pages 83-93
    3. Xiang-Sun Zhang
      Pages 95-136
    4. Xiang-Sun Zhang
      Pages 137-175
    5. Xiang-Sun Zhang
      Pages 177-195
  4. Neural Algorithms for Optimization

    1. Front Matter
      Pages 197-197
    2. Xiang-Sun Zhang
      Pages 199-241
    3. Xiang-Sun Zhang
      Pages 243-271
    4. Xiang-Sun Zhang
      Pages 273-288
    5. Xiang-Sun Zhang
      Pages 289-317
    6. Xiang-Sun Zhang
      Pages 319-333
  5. Back Matter
    Pages 335-371

About this book

Introduction

People are facing more and more NP-complete or NP-hard problems of a combinatorial nature and of a continuous nature in economic, military and management practice. There are two ways in which one can enhance the efficiency of searching for the solutions of these problems. The first is to improve the speed and memory capacity of hardware. We all have witnessed the computer industry's amazing achievements with hardware and software developments over the last twenty years. On one hand many computers, bought only a few years ago, are being sent to elementary schools for children to learn the ABC's of computing. On the other hand, with economic, scientific and military developments, it seems that the increase of intricacy and the size of newly arising problems have no end. We all realize then that the second way, to design good algorithms, will definitely compensate for the hardware limitations in the case of complicated problems. It is the collective and parallel computation property of artificial neural net­ works that has activated the enthusiasm of researchers in the field of computer science and applied mathematics. It is hard to say that artificial neural networks are solvers of the above-mentioned dilemma, but at least they throw some new light on the difficulties we face. We not only anticipate that there will be neural computers with intelligence but we also believe that the research results of artificial neural networks might lead to new algorithms on von Neumann's computers.

Keywords

Mathematica Optimization Theory algorithms combinatorial optimization linear optimization network networks neural networks nonlinear optimization optimization programming

Authors and affiliations

  • Xiang-Sun Zhang
    • 1
  1. 1.Academy of Mathematics and Systems, Institute of Applied MathematicsChinese Academy of SciencesChina

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4757-3167-5
  • Copyright Information Springer-Verlag US 2000
  • Publisher Name Springer, Boston, MA
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4419-4836-6
  • Online ISBN 978-1-4757-3167-5
  • Series Print ISSN 1571-568X
  • Buy this book on publisher's site