Optimization is a field important in its own right but is also integral to numerous applied sciences, including operations research, management science, economics, finance and all branches of mathematics-oriented engineering. Constrained optimization models are one of the most widely used mathematical models in operations research and management science. This book gives a modern and well-balanced presentation of the subject, focusing on theory but also including algorithims and examples from various real-world applications. The text is easy to read and accessible to anyone with a knowledge of multi-dimensional calculus, linear algebra and basic numerical methods. Detailed examples and counter-examples are provided - as are exercises, solutions and helpful hints, and Matlab/Maple supplements. The intended readership is advanced undergraduates, graduates, and professionals in any of the applied fields. Optimization is used in almost all branches of applied sciences today Text appeals to a wide readership because of its real life applications Self-contained text with a rich collection of detailed examples and two-color graphics to assist the reader in full comprehension Book includes many exercises, often supplemented by helpful hints or Matlab/Maple supplements INDICE: 1. Introduction: Examples of Optimization Problems, Historical Overview.- 2. Optimality Conditions: Convex Sets, Inequalities, Local First- and Second-Order Optimality Conditions, Duality.- 3. Unconstrained Optimization Problems: Elementary Search and Localization Methods, Descent Methods with Line Search, Trust Region Methods, Conjugate Gradient Methods, Quasi-Newton Methods.- 4. Linearly Constrained Optimization Problems: Linear and Quadratic Optimization, Projection Methods.- 5. Nonlinearly Constrained Optimization Methods: Penalty Methods, SQP Methods.- 6. Interior-Point Methods for Linear Optimization: The Central Path, Newton's Method for the Primal-Dual System, Path-Following Algorithms, Predictor-Corrector Methods.- 7. Semidefinite Optimization: Selected Special Cases, The S-Procedure, The Function log°det, Path-Following Methods, How to Solve SDO Problems?, Icing on the Cake: Pattern Separation via Ellipsoids.- 8. Global Optimization: Branch and Bound Methods, Cutting Plane Methods.- Appendices: A Second Look at the Constraint Qualifications, The Fritz John Condition, Optimization Software Tools for Teaching and Learning.- Bibliography.- Index of Symbols.- Subject Index.
- ISBN: 978-0-387-78976-7
- Editorial: Springer
- Encuadernacion: Cartoné
- Páginas: 402
- Fecha Publicación: 29/07/2010
- Nº Volúmenes: 1
- Idioma: Inglés