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A D.C. Approach to the Largest Empty Sphere Problem in Higher Dimension

  • Jianming Shi
  • Yamamoto Yoshitsugu
Part of the Nonconvex Optimization and Its Applications book series (NOIA, volume 7)

Abstract

In this paper, we present a d.c. approach for solving the largest empty sphere problem, i.e., given m points PhR n and a polytope maxmin \(\mathop {\max }\limits_{x \in D} \min \left\{ {\left\| {x - {p_h}} \right\|\left| {h = 1, \ldots ,m} \right.} \right\}.\). We reduce the problem to a global optimizational problem. Employing the special structure of this problem, our algorithm, which utilizes a combination of branch-and-bound and outer-inner-approximation, finds an optimal solution within finitely many iterations under a mild assumption.

Keywords

global optimizations d.c. approach largest empty sphere problem branch-and-bound method outer and inner approximation 

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Copyright information

© Kluwer Academic Publishers 1996

Authors and Affiliations

  • Jianming Shi
    • 1
  • Yamamoto Yoshitsugu
    • 1
  1. 1.Institute of Socio-Economic PlanningUniversity of TsukubaIbarakiJapan

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