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.

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