xvi PREFACE principle governing markets: the price for which supply equals de- mand is the price for which total social welfare is maximal. 3) Mathematical applications. The justification for mathemat- ical applications is less straightforward. There is--and always has been--a tendency to reach the essence of things: scientific curiosity compels some people to go to the bottom of the matter. For exam- ple, if you have obtained an upper or lower bound that suffices for practical purposes, then nevertheless you can go on to search for the sharpest one. 0.3 FOR WHOM IS THIS BOOK MEANT? · Short answer. A basic mathematical knowledge is sufficient to understand the topics covered in the book and to master the methods. This makes the book very useful for nonspecialists. On the other hand, more advanced readers and even experts might be surprised to see how all main results can be grounded on the so-called Fermat-Lagrange theorem. The book can be used for a wide range of courses on continuous optimization, from introductory to advanced, for any field for which optimiza- tion is relevant. The minimum goal would be to master the main tricks of finding analytical solutions of optimization prob- lems. These are explained in a few pages in appendix D, "Crash Course on Problem Solving." The maximal goal would be to get to the bottom of the subject, to get a complete understanding of all insights and to study all applications. · Detailed answer. This book is based on our research--resulting in many novel details--and on our teaching experience. Parts of this book have been tested in courses given at the departments of Mathematics and Economics of the Universities of Moscow and Rotterdam. The participants of these courses were students in Economics, Econometrics and Mathematics, Ph.D. students in Economics and Management Science, and Master's students in Maritime Economics. The aim is to introduce the reader, with- out requiring any previous knowledge of optimization, to the state of the art of solving concrete optimization problems. It is meant for beginners as well as for advanced readers and even for experts. The prerequisites are as follows: