Optimization-Theory and Practice

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.

Sommario

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.

Info autore

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).

Riassunto

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.

Testo aggiuntivo

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)

Relazione

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. Janácek, Zentralblatt)

Dettagli sul prodotto

• Autori: Wilhel Forst, Wilhelm Forst, Dieter Hoffmann
• Editore: Springer, Berlin
• Lingue: Inglese
• Formato: Tascabile
• Pubblicazione: 01.01.2016
• EAN: 9781493939336
• ISBN: 978-1-4939-3933-6
• Pagine: 402
• Dimensioni: 177 mm x 24 mm x 254 mm
• Peso: 804 g
• Illustrazioni: XVIII, 402 p.
• Serie: Springer Undergraduate Texts in Mathematics and Technology; Springer Undergraduate Texts i; Springer Undergraduate Texts in Mathematics and Technology
• Categorie: Scienze naturali, medicina, informatica, tecnica > Matematica > Altro; Algebra, B, Optimization, Mathematics and Statistics, Programming Techniques, Computational Mathematics and Numerical Analysis, Computer programming, Computer mathematics, Numerical analysis, Computational Science and Engineering, Maths for scientists, Mathematical optimization, Computer programming / software engineering, Computer science—Mathematics, Maths for computer scientists, Symbolic and Algebraic Manipulation