Observations on the Minimum Sphere Problem.

Abstract

For a subset A of Euclidean n-space, the location problem of finding the point x which minimizes the maximum distance d(x, a) for a in A may be interpreted as finding the smallest sphere which encloses A. Algorithms have previously been developed for the situations when A is finite or a polytope. Here we concentrate on interpretations and properties of the problem, particularly its relation to other problems: cases where the sphere problem is dual to that of finding a shortest vector in A, where there is a connection with a maximum moment-of-inertia problem, etc. Conjectures, relating the minimum sphere to points in A which define the diameter of A, are also discussed. (Author)

Open PDF

Document Details

Document Type
Technical Report
Publication Date
May 01, 1977
Accession Number
ADA051759

Entities

People

  • Donald Hearn

Organizations

  • University of Florida

Tags

Communities of Interest

  • Air Platforms
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Abstracts
  • Algorithms
  • Center Of Gravity
  • Convex Sets
  • Diameters
  • Engineering
  • Gravity
  • Industrial Engineering
  • Inertia
  • Military Research
  • Moment Of Inertia
  • Quadratic Programming
  • Security
  • Systems Engineering
  • Theorems
  • Triangles
  • Two Dimensional

Fields of Study

  • Mathematics

Readers

  • Approximation Theory.
  • Operations Research

Technology Areas

  • Space
  • Space - Spacecraft Maneuvers