Optimization—Theory and Practice

图书简介

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.

1. Introduction: Examples of Optimization Problems, HistoricalOverview.- 2. Optimality Conditions: Convex Sets, Inequalities, LocalFirst- 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 theCake: 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.

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Optimization—Theory and Practice（Springer Undergraduate Texts in Mathematics and Technology） 运筹学

Optimization—Theory and Practice（Springer Undergraduate Texts in Mathematics and Technology）
运筹学