Guler, Osman Foundations of Optimization

ISBN 13: 9780387344317

Foundations of Optimization

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9780387344317: Foundations of Optimization

Optimization is everywhere. It is human nature to seek the best option among all that are available. Nature, too, seems to be guided by optimization|many laws of nature have a variational character. Among geometric gures in the plane with a xed perimeter, the circle has the greatest area. Such isoperim- ric problems involving geometric gures date back to ancient Greece. Fermat's principle, discovered in 1629, stating that the tangent line is horizontal at a minimum point, seems to have in uenced the development of calculus. The proofs of Rolle's theorem and the mean value theorem in calculus use the Weierstrass theorem on the existence of maximizers and minimizers. The - troduction of the brachistochrone problem in 1696 by Johann Bernoulli had a tremendous impact on the development of the calculus of variations and in uenced the development of functional analysis. The variational character of laws of mechanics and optics were discovered in the seventeenth and ei- teenth centuries. Euler and Lagrange forged the foundations of the calculus of variations in the eighteenth century. In the nineteenth century, Riemann used Dirichlet's principle, which has a variational character, in his investigations in complex analysis. The simplex method for linear programming was disc- ered shortly after the advent of computers in the 1940s, and in uenced the subsequent development of mathematical programming. The emergence of the theory of optimal control in the 1950s was in response to the need for contr- ling space vehicles and various industrial processes.

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From the reviews:

“This book is an advanced graduate level text on the mathematical theory of optimization. … filled with many useful examples and counterexamples that provide intuition to support the more formal theorems and proofs. … There are also numerous exercises for the student. … The book will also be useful as a reference for researchers working in various areas of optimization.” (Brian Borchers, The Mathematical Association of America, October, 2010)

“Güler’s book … is intended for postgraduates or researchers in optimization theory; however, it is also suitable as a textbook in a first-year graduate level course. The book covers a wide range of mathematical tools and results concerning the fundamental principles of optimization in finite-dimensional spaces. … this book can be a solid reference textbook, useful for graduate students in applied mathematics, economics, engineering, operations research, etc., and, more generally, for anyone wishing to learn the essential mathematical principles of optimization theory.” (Giorgio Giorgi, Mathematical Reviews, Issue 2011 e)

"...this textbook presents the state of the art in the theory of continuous optimization in a very transparent and accessible way. Several results are proved in two or more independent ways to gain further insight into the problem structure, and to provide instructors with alternative ways of exposition. The book may be warmly recommended to graduate students and researchers in optimization, operations research, and other fields which apply optimization methods." (Zentralblatt Math, 2010)

Dalla quarta di copertina:

The book gives a detailed and rigorous treatment of the theory of optimization (unconstrained optimization, nonlinear programming, semi-infinite programming, etc.) in finite-dimensional spaces. The fundamental results of convexity theory and the theory of duality in nonlinear programming and the theories of linear inequalities, convex polyhedra, and linear programming are covered in detail. Over two hundred, carefully selected exercises should help the students master the material of the book and give further insight. Some of the most basic results are proved in several independent ways in order to give flexibility to the instructor. A separate chapter gives extensive treatments of three of the most basic optimization algorithms (the steepest-descent method, Newton’s method, the conjugate-gradient method). The first chapter of the book introduces the necessary differential calculus tools used in the book. Several chapters contain more advanced topics in optimization such as Ekeland’s epsilon-variational principle, a deep and detailed study of separation properties of two or more convex sets in general vector spaces, Helly’s theorem and its applications to optimization, etc. The book is suitable as a textbook for a first or second course in optimization at the graduate level. It is also suitable for self-study or as a reference book for advanced readers. The book grew out of author’s experience in teaching a graduate level one-semester course a dozen times since 1993. Osman Guler is a Professor in the Department of Mathematics and Statistics at University of Maryland, Baltimore County. His research interests include mathematical programming, convex analysis, complexity of optimization problems, and operations research.

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Osman Guler
Editore: Springer-Verlag New York Inc., United States (2010)
ISBN 10: 0387344314 ISBN 13: 9780387344317
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Descrizione libro Springer-Verlag New York Inc., United States, 2010. Hardback. Condizione libro: New. 2010 ed.. 239 x 160 mm. Language: English . Brand New Book. Optimization is everywhere. It is human nature to seek the best option among all that are available. Nature, too, seems to be guided by optimization|many laws of nature have a variational character. Among geometric gures in the plane with a xed perimeter, the circle has the greatest area. Such isoperim- ric problems involving geometric gures date back to ancient Greece. Fermat s principle, discovered in 1629, stating that the tangent line is horizontal at a minimum point, seems to have in uenced the development of calculus. The proofs of Rolle s theorem and the mean value theorem in calculus use the Weierstrass theorem on the existence of maximizers and minimizers. The - troduction of the brachistochrone problem in 1696 by Johann Bernoulli had a tremendous impact on the development of the calculus of variations and in uenced the development of functional analysis. The variational character of laws of mechanics and optics were discovered in the seventeenth and ei- teenth centuries. Euler and Lagrange forged the foundations of the calculus of variations in the eighteenth century. In the nineteenth century, Riemann used Dirichlet s principle, which has a variational character, in his investigations in complex analysis. The simplex method for linear programming was disc- ered shortly after the advent of computers in the 1940s, and in uenced the subsequent development of mathematical programming. The emergence of the theory of optimal control in the 1950s was in response to the need for contr- ling space vehicles and various industrial processes. Codice libro della libreria AAW9780387344317

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Osman Guler
Editore: Springer-Verlag New York Inc., United States (2010)
ISBN 10: 0387344314 ISBN 13: 9780387344317
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Descrizione libro Springer-Verlag New York Inc., United States, 2010. Hardback. Condizione libro: New. 2010 ed.. 239 x 160 mm. Language: English . Brand New Book. Optimization is everywhere. It is human nature to seek the best option among all that are available. Nature, too, seems to be guided by optimization|many laws of nature have a variational character. Among geometric gures in the plane with a xed perimeter, the circle has the greatest area. Such isoperim- ric problems involving geometric gures date back to ancient Greece. Fermat s principle, discovered in 1629, stating that the tangent line is horizontal at a minimum point, seems to have in uenced the development of calculus. The proofs of Rolle s theorem and the mean value theorem in calculus use the Weierstrass theorem on the existence of maximizers and minimizers. The - troduction of the brachistochrone problem in 1696 by Johann Bernoulli had a tremendous impact on the development of the calculus of variations and in uenced the development of functional analysis. The variational character of laws of mechanics and optics were discovered in the seventeenth and ei- teenth centuries. Euler and Lagrange forged the foundations of the calculus of variations in the eighteenth century. In the nineteenth century, Riemann used Dirichlet s principle, which has a variational character, in his investigations in complex analysis. The simplex method for linear programming was disc- ered shortly after the advent of computers in the 1940s, and in uenced the subsequent development of mathematical programming. The emergence of the theory of optimal control in the 1950s was in response to the need for contr- ling space vehicles and various industrial processes. Codice libro della libreria AAW9780387344317

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Guler, Osman
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Descrizione libro Springer-Verlag New York Inc., 2010. Condizione libro: New. This book covers the fundamental principles of optimization in finite dimensions. It develops the necessary material in multivariable calculus both with coordinates and coordinate-free, so recent developments such as semidefinite programming can be dealt with. Series: Graduate Texts in Mathematics. Num Pages: 442 pages, biography. BIC Classification: PBU. Category: (UU) Undergraduate. Dimension: 235 x 165 x 36. Weight in Grams: 828. . 2010. 1st. Hardcover. . . . . . Codice libro della libreria V9780387344317

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Descrizione libro Springer-Verlag New York Inc., New York, NY. hardback. Condizione libro: New. Codice libro della libreria 9780387344317

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Descrizione libro Springer-Verlag New York Inc. Condizione libro: New. This book covers the fundamental principles of optimization in finite dimensions. It develops the necessary material in multivariable calculus both with coordinates and coordinate-free, so recent developments such as semidefinite programming can be dealt with. Series: Graduate Texts in Mathematics. Num Pages: 442 pages, biography. BIC Classification: PBU. Category: (UU) Undergraduate. Dimension: 235 x 165 x 36. Weight in Grams: 828. . 2010. 1st. Hardcover. . . . . Books ship from the US and Ireland. Codice libro della libreria V9780387344317

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Descrizione libro Springer-Verlag New York Inc., 2006. HRD. Condizione libro: New. New Book. Shipped from UK in 4 to 14 days. Established seller since 2000. Codice libro della libreria BB-9780387344317

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Descrizione libro Springer-Verlag New York Inc., 2006. HRD. Condizione libro: New. New Book. Shipped from US within 10 to 14 business days. THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000. Codice libro della libreria I1-9780387344317

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Descrizione libro Condizione libro: New. Depending on your location, this item may ship from the US or UK. Codice libro della libreria 97803873443170000000

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Descrizione libro Springer, 2010. Condizione libro: New. Codice libro della libreria L9780387344317

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Descrizione libro Springer, 2010. Hardback. Condizione libro: NEW. 9780387344317 This listing is a new book, a title currently in-print which we order directly and immediately from the publisher. Codice libro della libreria HTANDREE0273279

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