Neural Networks in Optimization

1. Front Matter

   Pages i-xii

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2. Fundamental Concepts and Models of Optimization

   1. Front Matter

      Pages 1-1

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   2. Preliminaries

      • Xiang-Sun Zhang

      Pages 3-29

   3. Introduction to Mathematical Programming

      • Xiang-Sun Zhang

      Pages 31-51

   4. Algorithms for Unconstrained Nonlinear Programming

      • Xiang-Sun Zhang

      Pages 53-63

   5. Algorithms for Constrained Nonlinear Programming

      • Xiang-Sun Zhang

      Pages 65-80

3. Basic Artificial Neural Network Models

   1. Front Matter

      Pages 81-81

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   2. Introduction to Artificial Neural Network

      • Xiang-Sun Zhang

      Pages 83-93

   3. Feedforward Neural Networks

      • Xiang-Sun Zhang

      Pages 95-136

   4. Feedback Neural Networks

      • Xiang-Sun Zhang

      Pages 137-175

   5. Self-Organized Neural Networks

      • Xiang-Sun Zhang

      Pages 177-195

4. Neural Algorithms for Optimization

   1. Front Matter

      Pages 197-197

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   2. NN Models for Combinatorial Problems

      • Xiang-Sun Zhang

      Pages 199-241

   3. NN Models for Quadratic Programming Problems

      • Xiang-Sun Zhang

      Pages 243-271

   4. NN Models for General Nonlinear Programming

      • Xiang-Sun Zhang

      Pages 273-288

   5. NN Models for Linear Programming

      • Xiang-Sun Zhang

      Pages 289-317

   6. A Review on NN for Continuious Optimization

      • Xiang-Sun Zhang

      Pages 319-333

5. Back Matter

   Pages 335-371

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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.

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

• Academy of Mathematics and Systems, Institute of Applied Mathematics, Chinese Academy of Sciences, China

  Xiang-Sun Zhang

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