Abstract:
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This paper presents an algorithm to compute tight enclosures for the
range of a differentiable function f restricted to an interval
vector. The algorithm combines two different approaches: a
gradient-based method, and an optimization method. First, we use the
information contained in the gradient to compute enclosures for the
endpoints of the range of f. If these enclosures are not tight, we
apply an optimization method in order to get a more accurate result. |