Chebyshev Center of the Intersection of Balls: Complexity, Relaxation and Approximation.

We study the n-dimensional problem of finding the smallest ball enclosing the intersection of p given balls, the so-called Chebyshev center problem (CCB). It is a minimax optimization problem and the inner maximization is a uniform quadratic optimization problem (UQ). When p n. Finally, also based on (LP), we show that (CCB) is polynomially solved when either n or p-n(> 0) is fixed.