Classical Principles and Optimization Problems

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. Front Matter....Pages i-xiv Introduction....Pages 1-4 The Principle of Virtual Displacement. Problem of Mathematical Programming....Pages 5-24 The Detachment Principle and Optimization Methods....Pages 25-44 The Energy Theorem....Pages 45-67 Models for Systems of Linear Equations and Inequalities. Alternative Theorems.Models for Linear Programming Problems....Pages 68-108 Hodograph Method for Linear Programming Problems....Pages 109-140 Method of Shifting Elastic Constraints for Linear Programming Problems....Pages 141-158 Problem of Maximum Flow in Networks....Pages 159-183 Models and Methods for Solving Transportation Problem of Linear Programming....Pages 184-208 Methods of Decomposition of Linear Programming Problems....Pages 209-238 Gradient Methods....Pages 239-262 The Method of Aggregation of Constraints....Pages 263-293 Foundations of Thermodynamics....Pages 294-316 Equilibrium and Distribution of Resources....Pages 317-332 Models of Economic Equilibrium....Pages 333-371 Von Neumann’s Model of Economic Growth....Pages 372-401 Analytical Dynamics....Pages 402-434 Dynamics of Systems Under Elastic Constraints....Pages 435-456 Dynamical Problems of Optimal Control....Pages 457-504 Back Matter....Pages 505-513