| Foundations of Optimization 2010 Edition Contributor(s): Güler, Osman (Author) |
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ISBN: 0387344314 ISBN-13: 9780387344317 Publisher: Springer OUR PRICE: $71.20 Product Type: Hardcover - Other Formats Published: August 2010 Annotation: This book is intended as a textbook to be used in a first graduate level course, and covers the fundamental principals of optimization in finite dimensions. It develops the necessary background material in multivariable calculus using coordinates as well as in a coordinate-free manner, so that the recent developments such as semidefinite programming can be dealt with ease. All the standard topics of mathematical programming, such as necessary and sufficient optimality conditions for optimality, convex analysis and duality, are covered in great detail, often from multiple points of view. A distinctive feature of this book is its set of worked-out examples and problems, including hundreds of well-chosen problems and important examples. |
| Additional Information |
| BISAC Categories: - Science | Chemistry - General - Mathematics | Linear & Nonlinear Programming - Business & Economics | Operations Research |
| Dewey: 519.6 |
| LCCN: 2010932783 |
| Series: Springer Series in Operations Research and Financial Enginee |
| Physical Information: 1" H x 6.14" W x 9.21" (1.80 lbs) 442 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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. |