Practical Mathematical Optimization (eBook)

This book presents basic optimization principles and gradient-based algorithms to a general audience in a brief and easy-to-read form, without neglecting rigor. The work should enable professionals to apply optimization theory and algorithms to their own particular practical fields of interest, be it engineering, physics, chemistry, or business economics. Most importantly, for the first time in a relatively brief and introductory work, due attention is paid to the difficulties – such as noise, discontinuities, expense of function evaluations, and the existence of multiple minima – that often unnecessarily inhibit the use of gradient-based methods. In a separate chapter on new gradient-based methods developed by the author and his coworkers, it is shown how these difficulties may be overcome without losing the desirable features of classical gradient-based methods.

---

It is intended that this book be used in senior- to graduate-level semester courses in optimization, as offered in mathematics, engineering, com- puter science and operations research departments. Hopefully this book will also be useful to practising professionals in the workplace. The contents of the book represent the fundamental optimization mate- rial collected and used by the author, over a period of more than twenty years, in teaching Practical Mathematical Optimization to undergradu- ate as well as graduate engineering and science students at the University of Pretoria. The principal motivation for writing this work has not been the teaching of mathematics per se, but to equip students with the nec- essary fundamental optimization theory and algorithms, so as to enable them to solve practical problems in their own particular principal fields of interest, be it physics, chemistry, engineering design or business eco- nomics. The particular approach adopted here follows from the author's own personal experiences in doing research in solid-state physics and in mechanical engineering design, where he was constantly confronted by problems that can most easily and directly be solved via the judicious use of mathematical optimization techniques. This book is, however, not a collection of case studies restricted to the above-mentioned specialized research areas, but is intended to convey the basic optimization princi- ples and algorithms to a general audience in such a way that, hopefully, the application to their own practical areas of interest will be relatively simple and straightforward.