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Other titles in the Springer Optimization and Its Applications series:

Springer Optimization and Its Applications #51: Minisum Hyperspheres

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Springer Optimization and Its Applications #51: Minisum Hyperspheres Cover

 

Synopses & Reviews

Publisher Comments:

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.

Synopsis:

This book presents a self-contained introduction to the theory of minisum hyperspheres. This

Table of 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.- Bibliiography.- Index.

Product Details

ISBN:
9781441998064
Author:
Korner, Mark Christoph
Publisher:
Springer
Author:
Krner, Mark-Christoph
Author:
Körner, Mark-Christoph
Location:
New York, NY
Subject:
Geometry - General
Subject:
Convex Optimization
Subject:
Geometric Optimization
Subject:
Minisum Hypersphere Problem
Subject:
Geometry
Subject:
OPTIMIZATION
Subject:
Optimization <p>The first book dedicated to the topic of minisum hyperspheres</p><p>Provides a self-contained introduction to the topic</p><p>Includes an overview of the theory as well problem-solving strategies</p>
Subject:
Mathematics-Geometry and Trigonometry
Subject:
Mathematics
Subject:
Language, literature and biography
Subject:
mathematics and statistics
Subject:
Mathematical optimization
Copyright:
Edition Description:
2011
Series:
Springer Optimization and Its Applications
Series Volume:
51
Publication Date:
20110419
Binding:
HARDCOVER
Language:
English
Pages:
124
Dimensions:
235 x 155 mm

Related Subjects


Reference » Science Reference » Technology
Science and Mathematics » Mathematics » Applied
Science and Mathematics » Mathematics » Computer
Science and Mathematics » Mathematics » Functional Analysis
Science and Mathematics » Mathematics » General
Science and Mathematics » Mathematics » Geometry » Geometry and Trigonometry
Science and Mathematics » Mathematics » Topology

Springer Optimization and Its Applications #51: Minisum Hyperspheres Used Hardcover
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Product details 124 pages Springer - English 9781441998064 Reviews:
"Synopsis" by , This book presents a self-contained introduction to the theory of minisum hyperspheres. This
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