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.
Preface.-Preface to the Second Edition.-Introduction.-Fundamentals of Unconstrained Optimization.-Line Search Methods.-Trust-Region Methods.-Conjugate Gradient Methods.-Quasi-Newton Methods.-Large-Scale Unconstrained Optimization.-Calculating Derivatives.-Derivative-Free Optimization.-Least-Squares Problems.-Nonlinear Equations.-Theory of Constrained Optimization.-Linear Programming: The Simplex Method.-Linear Programming: Interior-Point Methods.-Fundamentals of Algorithms for Nonlinear Constrained Optimization.-Quadratic Programming.-Penalty and Augmented Lagrangian Methods.-Sequential Quadratic Programming.-Interior-Point Methods for Nonlinear Programming.-Background Material.- Regularization Procedure.