For a class of nonsmooth nonconvex multiobjective problems, we develop an inexact multiple proximal bundle method. In our approach instead of scalarization, we find descent direction for every objective function separately by utilizing the inexact proximal bundle method. Then we attempt to find a common descent direction for all objective functions. We study the effect of the inexactness of the objective and subgradient values on the new proposed method and obtain the reasonable convergence properties. We further consider a class of difficult nonsmooth nonconvex problems, made even more difficult by inserting the inexactness in the available information. At the end, to demonstrate the efficiency of the proposed algorithm, some encouraging numerical experiments are provided.

中文翻译：

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非光滑非凸多目标优化问题的不精确多近端丛算法

对于一类非光滑非凸多目标问题，我们开发了一种不精确的多近端丛方法。在我们的方法而不是标量化中，我们通过利用不精确近端束法分别找到每个目标函数的下降方向。然后我们尝试为所有目标函数找到一个共同的下降方向。我们研究了目标值和次梯度值的不精确性对新提出的方法的影响，并获得了合理的收敛性。我们进一步考虑一类困难的非光滑非凸问题，通过在可用信息中插入不精确性而变得更加困难。最后，为了证明所提出算法的效率，提供了一些令人鼓舞的数值实验。