Optimization—Theory and Practice

Wilhelm Forst, Dieter Hoffmann

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English

Springer-Verlag New York Inc.
26 July 2010

Algebra; Numerical analysis; Optimisation; Linear programming; Applied mathematics; Computer programming & software development; Maths for computer scientists

Series: Springer Undergraduate Texts in Mathematics and Technology

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.

By: Wilhelm Forst, Dieter Hoffmann
Imprint: Springer-Verlag New York Inc.
Country of Publication: United States
Edition: 2010 ed.
Dimensions: Height: 254mm, Width: 178mm, Spine: 25mm
Weight: 1.086kg
ISBN: 9780387789767
ISBN 10: 0387789766
Series: Springer Undergraduate Texts in Mathematics and Technology
Pages: 402
Publication Date: 26 July 2010
Audience: Professional and scholarly , Undergraduate
Format: Hardback
Publisher's Status: Active

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.

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).

Reviews for Optimization—Theory and Practice

From the reviews: The book is an excellent introduction to the world of continuous optimization. The authors are successful in balancing the theoretical background and the usable algorithms and optimization methods...The authors deserve an appreciation of the connection between theory and usage of mathematical tools as Matlab and Maple... [It] can be stated that this book constitutes a valuable guide for researchers and advanced students to the field of optimization. (J. Janacek, Zentralblatt) Few mathematics books manage to serve simultaneously the needs of many different types of readers, but this book by Frost (Ulm Univ., Germany) and Hoffmann (Univ. of Konstanz, Germany) offers satisfaction to everyone interested in optimization ! . book is fresh in conception and lucid in style and will appeal to anyone ! . invites the readers to think for themselves. ! Summing Up: Highly recommended. All levels/libraries. (D. V. Feldman, Choice, Vol. 48 (9), May, 2011)