Optimization-Theory and Practice

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 Includes supplementary material: sn.pub/extras

Autorentext

Dr. Wilhelm Forst is a professor in the Department of Numerical Analysis at the University of Ulm, Germany.

Dr. Dieter Hoffmann is a professor at the University of Konstanz, Germany.

Drs. Forst and Hoffman previously co-authored two German language books for Springer-Verlag: Funktionentheorie explore with Maple (2002) and Ordinary Differential Equations (2005).

Klappentext

Optimization is an important field in its own right but also plays a central role in numerous applied sciences, including operations research, management science, economics, finance, and engineering.

Optimization — Theory and Practice offers a modern and well-balanced presentation of various optimization techniques and their applications. The book's clear structure, sound theoretical basics complemented by insightful illustrations and instructive examples, makes it an ideal introductory textbook and provides the reader with a comprehensive foundation in one of the most fascinating and useful branches of mathematics.

Notable features include:

• Detailed explanations of theoretic results accompanied by supporting algorithms and exercises, often supplemented by helpful hints or MATLAB®/MAPLE® code fragments;
• an overview of the MATLAB® Optimization Toolbox and demonstrations of its uses with selected examples;

• accessibility to readers with a knowledge of multi-dimensional calculus, linear algebra, and basic numerical methods.
  Written at an introductory level, this book is intended for advanced undergraduates and graduate students, but may also be used as a reference by academics and professionals in mathematics and the applied sciences.

  Inhalt

  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.