Optimization—Theory and Practice de Wilhelm Forst

Optimization—Theory and Practice: Springer Undergraduate Texts in Mathematics and Technology

en Limba Engleză Hardback – 26 iul 2010

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.

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Specificații

ISBN-13: 9780387789767
ISBN-10: 0387789766
Pagini: 402
Ilustrații: XVIII, 402 p.
Dimensiuni: 178 x 254 x 25 mm
Greutate: 1.06 kg
Ediția:2010
Editura: Springer
Colecția Springer
Seria Springer Undergraduate Texts in Mathematics and Technology

Locul publicării:New York, NY, United States

Public țintă

Upper undergraduate

Cuprins

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.

Recenzii

From the book reviews:
“The book is a marvelous introduction to a wonderful part of mathematics. It is appealing, easy to understand and at the same time serious mathematics is covered. … It is certainly a good choice for required text in an introductory course on optimization.” (Péter Hajnal, Acta Scientiarum Mathematicarum (Szeged), Vol. 78 (1-2), 2012)
“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)
“Strong aspect of this book is the discussion of interior point methods for linear and semidefinite programming. … The book contains many illustrations, some of which are particularly helpful in visualizing the mathematical theory. … The required level of mathematical maturity makes it more suitable for a first graduate course in optimization. This book may be of interest to instructors who are looking for a textbook that emphasizes the mathematical theory of optimization, optimality conditions, and interior point methods for linear and semidefinite programming.” (Brain Borchers, The Mathematical Association of America, October, 2010)
"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 fieldof optimization." (J. Janáček, Zentralblatt)

Notă biografică

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).

Textul de pe ultima copertă

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.

Caracteristici

Optimization is used in almost all branches of applied sciences today Text appeals to a wide readership because of its real life applications Self-contained text with a rich collection of detailed examples and two-color graphics to assist the reader in full comprehension Book includes many exercises, often supplemented by helpful hints or Matlab/Maple supplements Includes supplementary material: sn.pub/extras

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