Classical principles and optimization problems
著者
書誌事項
Classical principles and optimization problems
（Mathematics and its applications, Soviet series）
D. Reidel Pub. Co. , Sold and distributed in the U.S.A. and Canada by Kluwer Academic Publishers, c1987
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注記
Includes references (p. 505-510) and indexes
内容説明・目次
内容説明
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.
目次
1. The principle of virtual displacement. Problem of mathematical programming..- 2. The detachment principle and optimization methods.- 3. The energy theorem.- 4. Models for systems of linear equations and inequalities. Alternative theorems. Models for linear programming problems..- 5. Hodograph method for linear programming problems.- 6. Method of shifting elastic constraints for linear programming problems.- 7. Problem of maximum flow in networks.- 8. Models and methods for solving transportation problem of linear programming.- 9. Methods of decomposition of linear programming problems.- 10. Gradient methods.- 11. The method of aggregation of constraints.- 12. Foundations of thermodynamics.- 13. Equilibrium and distribution of resources.- 14. Models of economic equilibrium.- 15. Von Neumann's model of economic growth.- 16. Analytical dynamics.- 17. Dynamics of systems under elastic constraints.- 18. Dynamical problems of optimal control.- References.- Name index.
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