Minisum Hyperspheres (Springer Optimization and Its Applications, 51) - Softcover

Körner, Mark-Christoph

Softcover

ISBN 10: 1461429188 ISBN 13: 9781461429180

Publisher: Springer, 2013

Synopsis

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 strategies.

About this title

From the Back Cover:

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.

Review:

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 interested in continuous location theory and/or distance geometry.” (Frank Plastria, Mathematical Reviews, Issue 2012 f)

About this edition

• Publisher: Springer
• Publication date: 2013
• ISBN 10: 1461429188
• ISBN 13: 9781461429180
• Binding: Paperback
• Number of pages: 124