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# Expansion and estimation of the range of nonlinear functions

Publikationstyp

Journal Article

Publikationsdatum

1996

Sprache

English

Author

Institut

TORE-URI

Enthalten in

Volume

65

Issue

216

Start Page

1503

End Page

1512

Citation

Mathematics of Computation 65 (216): 1503-1512 (1996)

Publisher DOI

Scopus ID

Many verification algorithms use an expansion f(x) ∈ f(x̃) + S · (x-x̃), f : ℝ → ℝ for x ∈ X, where the set of matrices S if usually computed as a gradient or by means of slopes. In the following, an expansion scheme is described which frequently yields sharper inclusions for S. This allows also to compute sharper inclusions for the range of f over a domain. Roughly speaking, f has to be given by means of a computer program. The process of expanding f can then be fully automatized. The function f need not be differentiable. For locally convex or concave functions special improvements are described. Moreover, in contrast to other methods, x̃ ∩ X may be empty without implying large overestimations for S. This may be advantageous in practical applications. n n