On Chebyshev Center of the Intersection of Two Ellipsoids
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.
KeywordsChebyshev 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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