Ebook: Physical Models and Equilibrium Methods in Programming and Economics
Author: B. S. Razumikhin (auth.)
- Tags: Mathematical Modeling and Industrial Mathematics
- Series: Mathematics and Its Applications 2
- Year: 1984
- Publisher: Springer Netherlands
- Edition: 1
- Language: English
- pdf
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.
Content:
Front Matter....Pages i-xv
Introduction....Pages 1-8
Equilibrium of Mechanical Systems with Linear Constraints and Linear Programming Problems....Pages 9-37
Equilibrium of Physical Systems and Linear Programming Problems....Pages 38-108
The Method of Redundant Constraints and Iterative Algorithms....Pages 109-141
The Principle of Removing Constraints....Pages 142-160
The Hodograph Method....Pages 161-178
The Method of Displacement of Elastic Constraints....Pages 179-194
Decomposition Methods for Linear Programming Problems....Pages 195-226
Nonlinear Programming....Pages 227-249
The Tangent Method....Pages 250-267
Models for Economic Equilibrium....Pages 268-304
Dynamic Economic Models....Pages 305-335
Optimal Control Problems....Pages 336-343
Back Matter....Pages 344-351
Content:
Front Matter....Pages i-xv
Introduction....Pages 1-8
Equilibrium of Mechanical Systems with Linear Constraints and Linear Programming Problems....Pages 9-37
Equilibrium of Physical Systems and Linear Programming Problems....Pages 38-108
The Method of Redundant Constraints and Iterative Algorithms....Pages 109-141
The Principle of Removing Constraints....Pages 142-160
The Hodograph Method....Pages 161-178
The Method of Displacement of Elastic Constraints....Pages 179-194
Decomposition Methods for Linear Programming Problems....Pages 195-226
Nonlinear Programming....Pages 227-249
The Tangent Method....Pages 250-267
Models for Economic Equilibrium....Pages 268-304
Dynamic Economic Models....Pages 305-335
Optimal Control Problems....Pages 336-343
Back Matter....Pages 344-351
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