  The $L_{\infty}$ star discrepancy is a measure for the regularity of a finite
set of points taken from $[0,1)^d$. Low discrepancy point sets are highly
relevant for Quasi-Monte Carlo methods in numerical integration and several
other applications. Unfortunately, computing the $L_{\infty}$ star discrepancy
of a given point set is known to be a hard problem, with the best exact
algorithms falling short for even moderate dimensions around 8. However,
despite the difficulty of finding the global maximum that defines the
$L_{\infty}$ star discrepancy of the set, local evaluations at selected points
are inexpensive. This makes the problem tractable by black-box optimization
approaches.
  In this work we compare 8 popular numerical black-box optimization algorithms
on the $L_{\infty}$ star discrepancy computation problem, using a wide set of
instances in dimensions 2 to 15. We show that all used optimizers perform very
badly on a large majority of the instances and that in many cases random search
outperforms even the more sophisticated solvers. We suspect that
state-of-the-art numerical black-box optimization techniques fail to capture
the global structure of the problem, an important shortcoming that may guide
their future development.
  We also provide a parallel implementation of the best-known algorithm to
compute the discrepancy.
