论文标题
局部Lipschitz多目标优化问题的有效下降方法
An efficient descent method for locally Lipschitz multiobjective optimization problems
论文作者
论文摘要
在本文中，我们提出了一种有效的下降方法，用于局部Lipschitz连续多目标优化问题（MOP）。通过结合对非平滑拖把的下降方向的计算与实用方法的理论结果来实现该方法。我们展示了满足帕累托最优条件的点的收敛。使用一组测试问题，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数量较大，但亚级别评估的总数较低。最后，我们证明我们的方法可以与细分算法结合使用，以计算整个非平滑拖把的整个帕累托集。
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 Mäkelä. 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.
