Minisum Hyperspheres / Edition 1

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This book presents a self-contained introduction to the theory of minisum hyperspheres. Thisspecialized researcharea within the larger field ofgeometric optimization is full of interesting and open problems.

This work provides an overview of the history of minisum hyperspheres as well as describes the best techniques for developing and solving minisum hypersphereproblems. Various related areas of geometric and nonlinear optimization are also discussed.

As the first publication devoted to this area of research, this work will be of greatinterest to graduate-level researchersstudyingminisum hypersphere problemsas well asmathematicians interested geometric optimization.

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Editorial Reviews

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“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)

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Product Details

  • ISBN-13: 9781441998064
  • Publisher: Springer New York
  • Publication date: 6/29/2011
  • Series: Springer Optimization and Its Applications Series, #51
  • Edition description: 2011
  • Edition number: 1
  • Pages: 116
  • Product dimensions: 6.20 (w) x 9.40 (h) x 0.50 (d)

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.

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