Nonlinear and Dynamic Programming An Introduction
This book is intended to provide an introductory text of Nonlinear and Dynamic Programming for students of managerial economics and operations research. The author also hopes that engineers, business executives, managers, and others responsible for planni
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Nonlinear and Dynamic Programming An Introduction
Springer-Verlag Wien New York
Prof. Dr. Sven Dan", Professor of Managerial Economics University of Copenhagen
This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means and storage in data banks. © 1975 by Springer-VerlagfWien
With 36 Figures
Library of Congress Cataloging In Publication Data. DaM, Sven. Nonlinear and dynamic pro· gramming. Bibliography: p. 1. Nonlinear programming. 2. Dynamic programming. I. Title. T57.8.D36. 519.7'6. 75-6503
ISBN 978·3·7091·8394·6 (eBook) ISBN 978·3·211·81289·1 DOl 10.1007/978·3·7091·8394·6
Preface This book is intended to provide an introductory text of Nonlinear and Dynamic Programming for students of managerial economics and operations research. The author also hopes that engineers, business executives, managers, and others responsible for planning of industrial operations may find it useful as a guide to the problems and methods treated, with a view to practical applications. The book may be considered as a sequel to the author's Linear Programming in Industry (1960, 4th revised and enlarged edition 1974), but it can be used independently by readers familiar with the elements of linear programming models and techniques. The two volumes constitute an introduction to the methods of mathematical programming and their application to industrial optimization problems. The author feels that the vast and ever-increasing literature on mathematical programming has not rendered an introductory exposition superfluous. The general student often tends to feel somewhat lost if he goes straight to the special literature; he will be better equipped for tackling real problems and using computer systems if he has acquired some previous training in constructing small-scale programming models and applying standard algorithms for solving them by hand. The book is intended to provide this kind of training, keeping the mathematics at the necessary minimum. The text contains numerous exercises. The reader should work out these problems for himself and check with the answers given at the end of the book. The text is based on lectures given at the University of Copenhagen. Students who have been exposed to earlier mimeographed versions have suggested improvements for which I am grateful. Chapter IV on quadratic programming is a revised version of an article in ErhvervsfJkonomisk Tidsskrijt, 1966. Copenhagen, January, 1975
Sven Dang
Contents I. Linear and Nonlinear Programming . . . . . . . . . . . . . . . . . . . . II. Elements of the Mathematical Theory of Nonlinear Programming ................. ......... ... ... ... ... ... .... A. Constrained Optimization ........ . . . . . . . . . . . . . . . . . . . . . . B. Kuhn-Tucker Optimization. . . . . . . . . . . . . . . . . . . . . . . . . . . . . III. Linearization of Nonlinear Programming Problems .
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