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.

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