Physical Models and Equilibrium Methods in Programming and Economics

1. Front Matter

   Pages i-xv

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2. Introduction

   • B. S. Razumikhin

   Pages 1-8

3. Equilibrium of Mechanical Systems with Linear Constraints and Linear Programming Problems

   • B. S. Razumikhin

   Pages 9-37

4. Equilibrium of Physical Systems and Linear Programming Problems

   • B. S. Razumikhin

   Pages 38-108

5. The Method of Redundant Constraints and Iterative Algorithms

   • B. S. Razumikhin

   Pages 109-141

6. The Principle of Removing Constraints

   • B. S. Razumikhin

   Pages 142-160

7. The Hodograph Method

   • B. S. Razumikhin

   Pages 161-178

8. The Method of Displacement of Elastic Constraints

   • B. S. Razumikhin

   Pages 179-194

9. Decomposition Methods for Linear Programming Problems

   • B. S. Razumikhin

   Pages 195-226

10. Nonlinear Programming

    • B. S. Razumikhin

    Pages 227-249

11. The Tangent Method

    • B. S. Razumikhin

    Pages 250-267

12. Models for Economic Equilibrium

    • B. S. Razumikhin

    Pages 268-304

13. Dynamic Economic Models

    • B. S. Razumikhin

    Pages 305-335

14. Optimal Control Problems

    • B. S. Razumikhin

    Pages 336-343

15. Back Matter

    Pages 344-351

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It isn't that they can't see Approach your problems from the solution. the right end and begin with It is that they can't see the the answers. Then one day, problem. perhaps you will find the final qu~stion. G. K. Chesterton. The Scandal of Father Brown ITh~ Point of 'The Hermit Clad in Crane Feathers' in R. van Gulik's a Pin'. The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. HowQvQr, thQ "tree" of knowledge of mathematics and related field does not grow only by putting forth new branches. It also happ~ns, quit~ often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathe­ matics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces.

• algorithm
• algorithms
• linear optimization
• model
• nonlinear optimization
• numerical methods
• programming
• thermodynamics

• Institute for Systems Studies, Academy of Sciences, Moscow, Russia

  B. S. Razumikhin

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