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Minisum hyperspheres

Author: Mark-Christoph Körner
Publisher: New York : Springer, ©2011.
Series: Springer optimization and its applications, v. 51.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Database:WorldCat
Summary:
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  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Körner, Mark-Christoph.
Minisum hyperspheres.
New York : Springer, 2011
(DLC) 2011929987
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Mark-Christoph Körner
ISBN: 9781441998071 1441998071 1441998063 9781441998064
OCLC Number: 745004895
Description: 1 online resource (viii, 116 pages).
Contents: 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.{u2013} Bibliiography.{u2013} Index.
Series Title: Springer optimization and its applications, v. 51.
Responsibility: Mark-Christoph Körner.
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Abstract:

This book presents a self-contained introduction to the theory of minisum hyperspheres. It is the first book dedicated to this topic, and includes an overview of the theory as well problem-solving  Read more...

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From the reviews: "This little book is fully devoted to what is known about the following median hypersphere problem and several of its variants ... . This book will be of interest to any researcher Read more...

 
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