On Chebyshev Center of the Intersection of Two Ellipsoids

  • Xiaoli Cen
  • Yong XiaEmail author
  • Runxuan Gao
  • Tianzhi Yang
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 991)


We study the problem of finding the smallest ball covering the intersection of two ellipsoids, which is also known as the Chebyshev center problem (CC). Semidefinite programming (SDP) relaxation is an efficient approach to approximate (CC). In this paper, we first establish the worst-case approximation bound of (SDP). Then we show that (CC) can be globally solved in polynomial time. As a by-product, one can randomly generate Celis-Dennis-Tapia subproblems having positive Lagrangian duality gap with high probability.


Chebyshev center Semidefinite programming Approximation bound Polynomial solvability CDT subproblem 



This research was supported by National Natural Science Foundation of China under grants 11822103, 11571029, 11771056 and Beijing Natural Science Foundation Z180005.


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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Xiaoli Cen
    • 1
  • Yong Xia
    • 1
    Email author
  • Runxuan Gao
    • 1
  • Tianzhi Yang
    • 1
  1. 1.LMIB of the Ministry of Education; School of Mathematics and System SciencesBeihang UniversityBeijingPeople’s Republic of China

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