We present an efficient descent method for unconstrained, locally Lipschitz multiobjective optimization problems. The method is realized by combining a theoretical result regarding the computation of descent directions for nonsmooth multiobjective optimization problems 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 with the multiobjective proximal bundle method by Mäkelä. The results indicate that our method is competitive while being easier to implement. Although the number of objective function evaluations is larger, the overall number of subgradient evaluations is smaller. Our method can be combined with a subdivision algorithm to compute entire Pareto sets of nonsmooth problems. Finally, we demonstrate how our method can be used for solving sparse optimization problems, which are present in many real-life applications.

我们为不受约束的局部Lipschitz多目标优化问题提供了一种有效的下降方法。该方法是通过将有关非平稳多目标优化问题的下降方向计算的理论结果与一种逼近目标函数次微分的实用方法相结合来实现的。我们证明了收敛到满足帕累托最优必要条件的点。使用一系列测试问题，我们将我们的方法与Mäkelä的多目标近端束方法进行了比较。结果表明，我们的方法具有竞争力，同时易于实施。尽管目标函数评估的次数较多，但次梯度评估的总数却较小。我们的方法可以与细分算法结合使用，以计算不光滑问题的整个帕累托集。最后，我们演示了如何将我们的方法用于解决稀疏优化问题，这些问题存在于许多实际应用中。