| Geometric Methods and Optimization Problems 1999 Edition Contributor(s): Boltyanski, Vladimir (Author), Martini, Horst (Author), Soltan, V. (Author) |
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ISBN: 0792354540 ISBN-13: 9780792354543 Publisher: Springer OUR PRICE: $284.99 Product Type: Hardcover - Other Formats Published: December 1998 Annotation: This book focuses on three disciplines of applied mathematics: control theory, location science and computational geometry. The authors show how methods and tools from convex geometry in a wider sense can help solve various problems from these disciplines. More precisely they consider mainly the tent method (as an application of a generalized separation theory of convex cones) in nonclassical variational calculus, various median problems in Euclidean and other Minkowski spaces (including a detailed discussion of the Fermat-Torricelli problem) and different types of partitionings of topologically complicated polygonal domains into a minimum number of convex pieces. Figures are used extensively throughout the book and there is also a large collection of exercises. Audience: Graduate students, teachers and researchers. |
| Additional Information |
| BISAC Categories: - Mathematics | Applied - Mathematics | Calculus - Mathematics | Geometry - Analytic |
| Dewey: 511.6 |
| LCCN: 98045185 |
| Series: Combinatorial Optimization |
| Physical Information: 1" H x 6.14" W x 9.21" (1.75 lbs) 432 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: VII Preface In many fields of mathematics, geometry has established itself as a fruitful method and common language for describing basic phenomena and problems as well as suggesting ways of solutions. Especially in pure mathematics this is ob- vious and well-known (examples are the much discussed interplay between lin- ear algebra and analytical geometry and several problems in multidimensional analysis). On the other hand, many specialists from applied mathematics seem to prefer more formal analytical and numerical methods and representations. Nevertheless, very often the internal development of disciplines from applied mathematics led to geometric models, and occasionally breakthroughs were b ed on geometric insights. An excellent example is the Klee-Minty cube, solving a problem of linear programming by transforming it into a geomet- ric problem. Also the development of convex programming in recent decades demonstrated the power of methods that evolved within the field of convex geometry. The present book focuses on three applied disciplines: control theory, location science and computational geometry. It is our aim to demonstrate how methods and topics from convex geometry in a wider sense (separation theory of convex cones, Minkowski geometry, convex partitionings, etc.) can help to solve various problems from these disciplines. |