Optimization—Theory and Practice

Wilhelm Forst, Dieter Hoffmann (Autoren)

Buch | Softcover

402 Seiten

2016 | Softcover reprint of the original 1st ed. 2010
Springer-Verlag New York Inc.
978-1-4939-3933-6 (ISBN)

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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.

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).

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.

Erscheinungsdatum	02.09.2016
Reihe/Serie	Springer Undergraduate Texts in Mathematics and Technology
Zusatzinfo	XVIII, 402 p.
Verlagsort	New York
Sprache	englisch
Maße	178 x 254 mm
Themenwelt	Mathematik / Informatik ► Informatik ► Theorie / Studium
	Mathematik / Informatik ► Mathematik ► Algebra
	Mathematik / Informatik ► Mathematik ► Analysis
	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
	Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie
	Mathematik / Informatik ► Mathematik ► Finanz- / Wirtschaftsmathematik
ISBN-10	1-4939-3933-5 / 1493939335
ISBN-13	978-1-4939-3933-6 / 9781493939336
Zustand	Neuware