Chebyshev center

In geometry, the Chebyshev center of a bounded set Q {displaystyle Q} having non-empty interior is the center of the minimal-radius ball enclosing the entire set Q {displaystyle Q} , or alternatively (and non-equivalently) the center of largest inscribed ball of Q {displaystyle Q} . In geometry, the Chebyshev center of a bounded set Q {displaystyle Q} having non-empty interior is the center of the minimal-radius ball enclosing the entire set Q {displaystyle Q} , or alternatively (and non-equivalently) the center of largest inscribed ball of Q {displaystyle Q} . In the field of parameter estimation, the Chebyshev center approach tries to find an estimator x ^ {displaystyle {hat {x}}} for x {displaystyle x} given the feasibility set Q {displaystyle Q} , such that x ^ {displaystyle {hat {x}}} minimizes the worst possible estimation error for x (e.g. best worst case). There exist several alternative representations for the Chebyshev center.Consider the set Q {displaystyle Q} and denote its Chebyshev center by x ^ {displaystyle {hat {x}}} . x ^ {displaystyle {hat {x}}} can be computed by solving: