Problems of optimization are pervasive in the modern world, appearing in science, social science, engineering, and business. Recent developments in optimization theory, especially those in mathematical programming and control theory, have therefore had many important areas of application and promise to have even wider usage in the future.
This book is intended as a self-contained introduction to and survey of static and dynamic optimization techniques and their application to economic theory. It is distinctive in covering both programming and control theory. While book-length studies exist for each topic covered here, it was felt that a book covering all these topics would be useful in showing their important interrelationships and the logic of their development. Because each chapter could have been a book in its own right, it was necessary to be selective. The emphasis is on presenting as clearly as possible the problem to be treated, and the best method of attack to enable the reader to use the techniques in solving problems. Space considerations precluded inclusion of some rigorous proofs, detailed refinements and extensions, and special cases; however, they are indirectly covered in the footnotes, problems, appendices, and bibliographies. While some problems are exercises in manipulating techniques, most are teaching or research problems, suggesting new ideas and offering a challenge to the reader. Most chapters contain a bibliography, and the most important references are indicated in the first footnote of each chapter. The most important equations are numbered in bold face type.