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This book presents a self-contained introduction to the theory of minisum hyperspheres. This specialized research area within the larger field of geometric 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 hypersphere problems. 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 great interest to graduate-level researchers studying minisum hypersphere problems as well as mathematicians interested geometric optimization.
List 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.
Summary
This book presents a self-contained introduction to the theory of minisum hyperspheres. This specialized research area within the larger field of geometric 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 hypersphere problems. 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 great interest to graduate-level researchers studying minisum hypersphere problems as well as mathematicians interested geometric optimization.
Additional text
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)
Report
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)
