Readers will find an elementary introduction to classical nonlinear optimization problems and methods for their solution in this book. The contents start from optimality conditions for unconstrained problems and describe the most common methods for various types of optimization problems (least squares, gradient methods, Newton iteration). Then, the author moves on to convex problems where the corresponding questions are addressed as well.
The book covers just as much of the theory as the reader needs to get a feeling for the obstacles that one has to overcome. Based on this theory, Beck then carefully guides the reader through the construction of the commonly used algorithms, thoroughly describing the ways in which the obstacles are tackled and which particular features of typical applications are exploited. Lots of examples are given, often with very helpful graphical illustrations that provide detailed insight. These examples strongly support the readers in their quest for understanding how the solution methods work. Many of the algorithms given in the book are stated in the form of MATLAB programs; the source code is available for download from the book’s companion web site. This is a very useful feature of the book that allows readers to immediately experiment with the given methods for themselves.
The style of writing is very pleasant and readable for novices in this area. The material is accessible not only to mathematicians, but also to researchers from other fields of science who need to find suitable algorithms for solving the optimization problems that arise in their daily work. A particularly appealing component of the book is the brief section containing bibliographical remarks with respect to each chapter. In this section, Beck gives additional comments and pointers to advanced literature for readers who are interested in a deeper study of the theoretical aspects or in more advanced algorithms. I recommend the book to scientists from all disciplines and to graduate or advanced undergraduate students who want to learn about applied mathematical optimization.
