Beyond Interval Uncertainty: Taking Constraints into Account
For set information, in addition to the interval bounds on each variables x1,..., x n , we may have additional information: e.g., we may know that the actual values should satisfy a constraint g(x1,..., x n ) ≤ g0. As we have mentioned earlier, usually, we know the approximate values of x i , so we can safely replace the function g(x1,..., x n ) by, e.g., the first two terms in its Taylor expansion. In this case, the constraint becomes quadratic, and – in a realistic case when this constraint describes a bounded set – the set of all the tuples x = (x1,..., x n ) that satisfy this constraint forms an ellipsoid. In this case, in addition to knowing that the actual tuple x belongs to the box, we also know that it belongs to the ellipsoid – i.e., that the set of possible values of this tuple is an intersection of the box and the ellipsoid. Such a situation is analyzed in this chapter.
KeywordsLinear Function Taylor Expansion Linear Time Interval Uncertainty Interval Bound
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