Classical Principles and Optimization Problems

1. Front Matter

   Pages i-xiv

   PDF

2. Introduction

   • B. S. Razumikhin

   Pages 1-4

3. The Principle of Virtual Displacement. Problem of Mathematical Programming

   • B. S. Razumikhin

   Pages 5-24

4. The Detachment Principle and Optimization Methods

   • B. S. Razumikhin

   Pages 25-44

5. The Energy Theorem

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   Pages 45-67

6. Models for Systems of Linear Equations and Inequalities. Alternative Theorems.Models for Linear Programming Problems

   • B. S. Razumikhin

   Pages 68-108

7. Hodograph Method for Linear Programming Problems

   • B. S. Razumikhin

   Pages 109-140

8. Method of Shifting Elastic Constraints for Linear Programming Problems

   • B. S. Razumikhin

   Pages 141-158

9. Problem of Maximum Flow in Networks

   • B. S. Razumikhin

   Pages 159-183

10. Models and Methods for Solving Transportation Problem of Linear Programming

    • B. S. Razumikhin

    Pages 184-208

11. Methods of Decomposition of Linear Programming Problems

    • B. S. Razumikhin

    Pages 209-238

12. Gradient Methods

    • B. S. Razumikhin

    Pages 239-262

13. The Method of Aggregation of Constraints

    • B. S. Razumikhin

    Pages 263-293

14. Foundations of Thermodynamics

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    Pages 294-316

15. Equilibrium and Distribution of Resources

    • B. S. Razumikhin

    Pages 317-332

16. Models of Economic Equilibrium

    • B. S. Razumikhin

    Pages 333-371

17. Von Neumann’s Model of Economic Growth

    • B. S. Razumikhin

    Pages 372-401

18. Analytical Dynamics

    • B. S. Razumikhin

    Pages 402-434

19. Dynamics of Systems Under Elastic Constraints

    • B. S. Razumikhin

    Pages 435-456

20. Dynamical Problems of Optimal Control

    • B. S. Razumikhin

    Pages 457-504

Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, tbat they can't see the problem. perbaps you will find the fina\ question. G. K. Chesterton. The Scandal of Father 'The Hermit Clad in Crane Feathers' in R. Brown 'The point of a Pin'. van GuJik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite 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 mathematics 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. And in addition to this there are such newemerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.

• Homotopy
• Host
• Lemma
• algebraic geometry
• distribution
• electrical engineering
• filtering
• geometry
• graphs
• homotopy theory
• knowledge
• mathematical programming
• measure
• measure theory
• programming

• Institute for Systems Studies, Moscow, USSR

  B. S. Razumikhin

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