Minisum Hyperspheres

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.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.