Bounds on f Sample Clauses

Bounds on f. ≤ ≤ This library provides a way to specify further bounds on the values of the interpolant Lo(x) g(x) Up(x). These bounds are included into the routines for calculation of the bounds Xxxxxx and Hlower, as well as in all optimization problems as additional constraints Lo(xk) ≤ yk + rk ≤ Up(xk), added to problems such as (2.7). ∈ ≥ Computation of these extra bounds could involve sophisticated algo- rithms, but it is transparent for the LibLip library. These bounds frequently arise when one has to ensure that the interpolant takes certain values at a sub- set of points, or is bounded. For example, when interpolating bivariate data and ensuring that f (x, 0) = f (0, x) = x, x [0, 1] and f (x, y) max(x, y). The member variable UseOtherBounds must be set to 1, and the vir- tual functions ExtraLowerBound() and ExtraUpperBound() should be im- plemented in a class derived from SLipInt (see the description of the library).
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