  In this article, we present an efficient descent method for locally Lipschitz
continuous multiobjective optimization problems (MOPs). The method is realized
by combining a theoretical result regarding the computation of descent
directions for nonsmooth MOPs with a practical method to approximate the
subdifferentials of the objective functions. We show convergence to points
which satisfy a necessary condition for Pareto optimality. Using a set of test
problems, we compare our method to the multiobjective proximal bundle method by
M\"akel\"a. The results indicate that our method is competitive while being
easier to implement. While the number of objective function evaluations is
larger, the overall number of subgradient evaluations is lower. Finally, we
show that our method can be combined with a subdivision algorithm to compute
entire Pareto sets of nonsmooth MOPs.
