Numerical Optimization

Numerical Optimization presents a comprehensive and up-to-date description of the most effective methods in continuous optimization. It responds to the growing interest in optimization in engineering, science, and business by focusing on the methods that are best suited to practical problems. Drawing on their experiences in teaching, research, and consulting, the authors have produced a textbook that will be of interest to students and practitioners alike. Each chapter begins with the basic concepts and builds up gradually to the best techniques currently available. Because of the emphasis on practical methods, as well as the extensive illustrations and exercises, the book is accessible to a wide audience. It can be used as a graduate text in engineering, operations research, mathematics, computer science, and business. It also serves as a handbook for researchers and practitioners in the field. Above all, the authors have strived to produce a text that is pleasant to read, informative, and rigorous - one that reveals both the beautiful nature of the discipline and its practical side.

For the second edition, the book has been brought up-to-date by adding new topics that have become important since the publication of the first edition, such as the nonlinear interior methods and filter methods. The authors have broadened the scope of the book by including a new chapter on derivative-free methods for optimization, which are used widely in practice and are the focus of much current research. An extensive reorganization and revision of the chapters on unconstrained optimization has been made. Large-scale optimization is treated more extensively. Significant changes have been made to the constrained optimization section. The chapter on theory of constrained optimization was revised and streamlined, and a section on duality added. The linear programming chapters were reorganized and modernized, and contain important new additions concerning dual simplex, presolving, and practical aspects of interior-point methods. New, modern treatments of topics such as sequential quadratic programming, augmented Lagrangian, and barrier methods have been added. Iterative linear algebra techniques in the constrained optimization context are treated more extensively. Lesspractical material (e.g., nonconvex quadratic programming, SQP or equality constraints) was reduced. Finally, many new exercises have been added to existing chapters.

Reviews of the first edition:

Mathematical Reviews: " I find the book... to be a well-written treatment of continuous nonlinear optimization and I would recommend its use for upper level undergraduate or graduate level courses in nonlinear optimization. The book is sufficiently detailed to be useful to researchers, but its real merit is as an educational resource."

SIAM: "[The] reviewer certainly plans to adopt the text (which contains many useful problems) for his own course and looks forward to a second edition addressing some of the issues raised here."

MMOR Mathematical Methods of Operations Research: "The book looks very suitable in an graduate-level course in optimization for students in mathematics, operations research, engineering, and others. Moreover, it seems to be very helpful to do some self-studies in optimization, to complete own knowledge and can be a source of new ideas. Because of the wide range of optimization problems considered and the large number of algorithms, the book is also of high interest for practitioners. Consequently, I recommend this excellent book to everyone who is interested in optimization problems."