Approaches to the Theory of Optimization

Optimization is concerned with finding the best (optimal) solution to mathematical problems that may arise in economics, engineering, the social sciences and the mathematical sciences. As is suggested by its title, this book surveys various ways of penetrating the subject. The author begins with a selection of the type of problem to which optimization can be applied and the remainder of the book develops the theory, mainly from the viewpoint of mathematical programming. To prevent the treatment becoming too abstract, subjects which may be considered 'unpractical' are not touched upon. The author gives plausible reasons, without forsaking rigor, to show how the subject develops 'naturally'. Professor Ponstein has provided a concise account of optimization which should be readily accessible to anyone with a basic understanding of topology and functional analysis. Advanced students and professionals concerned with operations research, optimal control and mathematical programming will welcome this useful and interesting book.

A concise account which finds the optimal solution to mathematical problems arising in economics, engineering, the social and mathematical sciences.

Preface; List of symbols; 1. Approaching optimization by means of examples; 2. An intuitive approach to mathematical programming; 3. A global approach by bifunctions; 4. A global approach by conjugate duality; 5. A local approach for optimization problems in Banach spaces; 6. Some other approaches; 7. Some applications; Appendices; Comments on the text and related literature; References; Index.