  The paper presents a new descent algorithm for locally Lipschitz continuous
functions $f:X\to\mathbb{R}$. The selection of a descent direction at some
iteration point $x$ combines an approximation of the set-valued gradient of $f$
on a suitable neighborhood of $x$ (recently introduced by Mankau & Schuricht)
with an Armijo type step control. The algorithm is analytically justified and
it is shown that accumulation points of iteration points are critical points of
$f$. Finally the algorithm is tested for numerous benchmark problems and the
results are compared with simulations found in the literature.
