Minisum hyperspheres
This volume presents a self-contained introduction to the theory of minisum hyperspheres. The minisum hypersphere problem is a generalization of the famous Fermat-Torricelli problem. The problem asks for a hypersphere minimizing the weighted sum of distances to a given point set. In the general fram...
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| Autor principal: | |
|---|---|
| Format: | Livre numérique |
| Idioma: | Anglais |
| Publicat: |
New York, NY :
Springer New York
[20..].
Cham : Springer Nature |
| Edició: | 1st ed. 2011. |
| Col·lecció: | Springer Optimization and Its Applications
51 |
| Matèries: | |
| Accés en línia: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Nota: |
Description d'après consultation du 15 mai 2012 Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Minisum hyperspheres, Mark-Christoph Körner, New York, Springer, 2011, 1 vol. (VII - 116 p.), Springer optimization and its applications, 978-1-441-99806-4 • Minisum Hyperspheres, Texte imprimé, 9781461429180 • Minisum Hyperspheres, Texte imprimé, 9781441998088 |
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| 100 | 1 | |a Körner, Mark-Christoph. | |
| 245 | 1 | 0 | |a Minisum hyperspheres |c Mark-Christoph Körner. |
| 250 | |a 1st ed. 2011. | ||
| 260 | |a New York, NY : |b Springer New York. | ||
| 260 | |a Cham : |b Springer Nature, |c [20..]. | ||
| 490 | 0 | |a Springer Optimization and Its Applications |v 51 |x 1931-6836 | |
| 500 | |a Description d'après consultation du 15 mai 2012 | ||
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 504 | |a Bibliogr. p. 109-113 Index p. 114-115 | ||
| 505 | 1 | |a -Preface 1. Basic Concepts (Circles and Hyperspheres, Minisum Hyperspheres, Mathematical Preliminaries, Finite Dominating Sets) 2. Euclidean Minisum Hyperspheres (Basic Assumptions, Distance, Degenerated Solutions, Existence of Optimal Solutions, Incidence Properties, Solution Approaches for the Planar Case, Concluding Remarks) 3. Minisum Hyperspheres in Normed Spaces (Basic Assumptions, Distance, Degenerated Solutions, Existence of Minisum Hyperspheres, Incidence Properties, Polyhedral Norms in the Plane, Concluding Remarks) 4. Minisum Circle Problem with Unequal Norms (Basic Assumptions, Distance, Properties of Minisum Circles, Polyhedral Norms, Concluding Remarks) 5. Minisum Rectangles in a Manhattan Plane (Basic Assumptions, Notations, Point-Rectangle Distance, Restricted Problems, Unrestricted Problem, Concluding Remarks) 6. Extensions.- Bibliiography.- Index. | |
| 506 | |a Accès en ligne pour les établissements français bénéficiaires des licences nationales | ||
| 506 | |a Accès soumis à abonnement pour tout autre établissement | ||
| 506 | |a Conditions particulières de réutilisation pour les bénéficiaires des licences nationales. https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 | ||
| 520 | |a This volume presents a self-contained introduction to the theory of minisum hyperspheres. The minisum hypersphere problem is a generalization of the famous Fermat-Torricelli problem. The problem asks for a hypersphere minimizing the weighted sum of distances to a given point set. In the general framework of finite dimensional real Banach spaces, the minisum hypersphere problem involves defining a hypersphere and calculating the distance between points and hyperspheres. The theory of minisum hyperspheres is full of interesting open problems which impinge upon the larger field of geometric optimization. This work provides an overview of the history of minisum hyperspheres as well as describes the best techniques for analyzing and solving minisum hypersphere problems. Related areas of geometric and nonlinear optimization are also discussed. Key features of Minisum Hyperspheres include: -assorted applications of the minisum hypersphere problem - a discussion on the existence of a solution to the problem with respect to Euclidean and other norms - several proposed extensions to the problem, including a highlight of positive and negative weights and extensive facilities extensions This work is the first book devoted to this area of research and will be of great interest to graduate students and researchers studying the minisum hypersphere problems as well as mathematicians interested in geometric optimization. | ||
| 650 | |a Optimisation mathématique | ||
| 650 | |a Espaces linéaires normés | ||
| 650 | |a Banach, Espaces de | ||
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| 776 | 0 | |t Minisum Hyperspheres |b Texte imprimé |z 9781461429180 | |
| 776 | 0 | |t Minisum Hyperspheres |b Texte imprimé |z 9781441998088 | |
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