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A First Course in Optimization Theory
This book introduces students to optimization theory and its use in economics and allied disciplines. The first of its three parts examines the existence of solutions to optimization problems in Rn, and how these solutions may be identified. The second part explores how solutions to optimization problems change with changes in the underlying parameters, and the last part provides an extensive description of the fundamental principles of finite- and infinite-horizon dynamic programming. A preliminary chapter and three appendices are designed to keep the book mathematically self-contained.
376 pages, Paperback
First published June 13, 1996
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Displaying 1 - 5 of 5 reviews
September 14, 2017
The book is amazing and is a must read for Researchers, who want to apply mathematical models in their research. I have just begun with reading the book.
July 16, 2019
Opmization-ыг маш гоё intuitive байдлаас нь заасан ном байна.
May 29, 2015
An excellent book on optimization theory, I can recommend it without hesitation. The book starts out with introducing the problem of optimization in Euclidean spaces before delving into area which undergraduate students/high school students identify with optimization: Setting the first derivative to zero. In later chapters, the book covers constrained optimization (Langrange and Karush-Kuhn-Tucker), convex optimization, quasi-convex optimization (which is rarely covered in related books, as far as I know), parameterized optimization and dynamic programming.
One of the best chapters of this book are those on constrained optimization: The theorems of Langrange and Kuhn-Tucker are derived, together with a cook-book procedure on how to apply them, and thorough explanation why they often work and in which cases they don't. I really appreciated all results in the book being rigorously proved, not shying away from difficult mathematics -- the book contains a very generous chapter on mathematical preliminaries, making sure it is self-contained. The book also covers apparently totally unrelated topics, such as fixed-point theorems (Tarski, Brouwer) -- only to proof the existence of Nash equilibria as a corollary. Another great feature is the huge amount of short examples, illustrating why certain conditions are necessary for lemmas and theorems. Longer examples based on economics are re-used throughout the book, making an absolutely consistent picture.
One of the best chapters of this book are those on constrained optimization: The theorems of Langrange and Kuhn-Tucker are derived, together with a cook-book procedure on how to apply them, and thorough explanation why they often work and in which cases they don't. I really appreciated all results in the book being rigorously proved, not shying away from difficult mathematics -- the book contains a very generous chapter on mathematical preliminaries, making sure it is self-contained. The book also covers apparently totally unrelated topics, such as fixed-point theorems (Tarski, Brouwer) -- only to proof the existence of Nash equilibria as a corollary. Another great feature is the huge amount of short examples, illustrating why certain conditions are necessary for lemmas and theorems. Longer examples based on economics are re-used throughout the book, making an absolutely consistent picture.
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December 10, 2010nice intro to optimization
July 9, 2012
great introduction reading, my favourite are the chapters about comparative statics.
Displaying 1 - 5 of 5 reviews
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