General Mathematics


Universal Optimization and Its Application

Authors: Alexander Bolonkin

The book consists of three parts. The first part describes new method of optimization that has the advantages at greater generality and flexibility as well as the ability to solve complex problems which other methods cannot solve. This method, called the “Method of Deformation of Functional (Extreme)”, solves for a total minimum and finds a solution set near the optimum. Solutions found by this method can be exact or approximate. Most other methods solve only for a unique local minimum. The ability to create a set of solutions rather than a unique solution has important practical ramifications in many designs, economic and scientific problems because a unique solution usually is difficult to realize in practice. This method has the additional virtue of a simple proof, one that is useful for studying other methods of optimization, since most other methods can be delivered from the Method of Deformation. The mathematical methods used in the book allow calculating special slipping and breaking optimal curves, which are often encountered in problems of optimal control. The author also describes the solution of boundary problems in optimization theory. The mathematical theory is illustrated by several examples. The book is replete with exercises and can be used as a text-book for graduate courses. In fact the author has lectured on this theory using this book for graduate and post-graduate students in Moscow Technical University. The second part of the book is devoted to applications of this method to technical problems in aviation, space, aeronautics, control, automation, structural design, economic, games, theory of counter strategy and etc. Some of the aviation, aeronautic, and control problems are examined: minimization of energy, exact control, fuel consumption, heating of re-entry space ship in the atmosphere of planets, the problems of a range of aircraft, rockets, dirigibles, and etc. Some of the economic problems are considered, for example, the problems of a highest productivity, the problem of integer programming and the problem of linear programming. Many economic problems may be solved by the application of the Method to the Problems of non-cooperative games. The third part of the book contains solutions of complex problems: optimal thrust angle for different flight regimes, optimal trajectories of aircraft, aerospace vehicles, and space ships, design of optimal regulator, linear problems of optimal control. This book is intended for designers, engineers, researchers, as well as specialists working on problems of optimal control, planning, or the choosing of optimal strategy. For engineers the book provides methods of computation of the optimal construction and control mechanisms, and optimal flight trajectories. In addition, the book will be useful to students of mathematics, general engineering, and economic. English translation is not full. Full text is in Russian referances.

Comments: 159 Pages.

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[v1] 2017-04-14 19:06:31

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