verry.optimize.branchbound_scalar#

verry.optimize.branchbound_scalar(fun, domain, fprime=True, xtol=inf, ytol=0.0, max_iter=16)#

Find the minimum of the univariate scalar-valued function by repeatedly dividing the interval.

Parameters:

  • fun (Callable) – Function to be optimized.

  • domain (Interval) – Interval in which to search for the minimum value.

  • fprime (Callable | bool, optional) – Derivative of fun (the default is deriv(fun)). If fprime is False, The differentiability of fun is not assumed.

  • xtol (default=inf) – Absolute tolerance.

  • ytol (default=0.0) – Relative tolerance.

  • max_iter (int, default=16) – Maximum number of iterations.

Returns:

  • r0 (Interval) – Interval containing the minimum value.

  • r1 (list[Interval]) – Intervals at which fun may take a minimum value.

Warning

fun must be a \(C^1\)-function on domain if fprime is not False. Futhermore, fun must neither be a constant nor contain conditional branches (cf. Common pitfalls).

See also

verry.autodiff.deriv

Examples

>>> from verry import FloatInterval as FI
>>> y, x = branchbound_scalar(lambda x: x**3 - 2 * x + 3, FI(0, 2))
>>> print(format(y, ".3f"))
[1.911, 1.912]
>>> print(format(x[0], ".3f"))
[0.816, 0.817]
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