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Chebyshev center
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Chebyshev center : ウィキペディア英語版
Chebyshev center

In geometry, the Chebyshev center of a bounded set Q having non-empty interior is the center of the minimal-radius ball enclosing the entire set Q, or alternatively (and non-equivalently) the center of largest inscribed ball of Q.〔
In the field of parameter estimation, the Chebyshev center approach tries to find an estimator \hat x for x given the feasibility set Q , such that \hat x minimizes the worst possible estimation error for x (e.g. best worst case).
== Mathematical representation ==
There exist several alternative representations for the Chebyshev center.
Consider the set Q and denote its Chebyshev center by \hat. \hat can be computed by solving:
: \min_ \max_ \left\| x - \hat x \right\|^2.
Despite these properties, finding the Chebyshev center may be a hard numerical optimization problem. For example, in the second representation above, the inner maximization is non-convex if the set ''Q'' is not convex.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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