Optimization—Theory and Practice [electronic resource] / by Wilhelm Forst, Dieter Hoffmann.
Contributor(s): Hoffmann, Dieter [author.] | SpringerLink (Online service)Material type: TextSeries: Springer Undergraduate Texts in Mathematics and Technology: Publisher: New York, NY : Springer New York, 2010Description: XVIII, 402 p. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9780387789774Subject(s): Mathematics | Computer programming | Computer science -- Mathematics | Algebra | Computer mathematics | Mathematical optimization | Mathematics | Optimization | Algebra | Programming Techniques | Symbolic and Algebraic Manipulation | Computational Mathematics and Numerical Analysis | Computational Science and EngineeringAdditional physical formats: Printed edition:: No titleDDC classification: 519.6 LOC classification: QA402.5-402.6Online resources: Click here to access online
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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.
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.