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In this article, we present an efficient descent method for locally Lipschitzcontinuous multiobjective optimization problems (MOPs). The method is realizedby combining a theoretical result regarding the computation of descentdirections for nonsmooth MOPs with a practical method to approximate thesubdifferentials of the objective functions. We show convergence to pointswhich satisfy a necessary condition for Pareto optimality. Using a set of testproblems, we compare our method to the multiobjective proximal bundle method byM\"akel\"a. The results indicate that our method is competitive while beingeasier to implement. While the number of objective function evaluations islarger, the overall number of subgradient evaluations is lower. Finally, weshow that our method can be combined with a subdivision algorithm to computeentire Pareto sets of nonsmooth MOPs.

An efficient descent method for locally Lipschitz multiobjective optimization problems