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基本説明
Gives a modern and well-balanced presentation of the subject, focusing on theory but also including algorithms and examples from various real-world applications. The text is easy to read and accessible to anyone with knowledge of multi-dimensional calculus, linear algebra and basic numerical methods.
Full Description
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.
Contents
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 logodet, 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.
