In this paper, we propose an adaptation of the classical augmented Lagrangian method for dealing with multi-objective optimization problems. Specifically, after a brief review of the literature, we give a suitable definition of Augmented Lagrangian for equality and inequality constrained multi-objective problems. We exploit this object in a general computational scheme that is proved to converge, under mild assumptions, to weak Pareto points of such problems. We then provide a modified version of the algorithm which is more suited for practical implementations, proving again convergence properties under reasonable hypotheses. Finally, computational experiments show that the proposed methods not only do work in practice, but are also competitive with respect to state-of-the-art methods.

中文翻译：

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一种用于多目标优化的增强拉格朗日算法

在本文中，我们提出了经典的增强拉格朗日方法的一种改进方案，用于处理多目标优化问题。具体来说，在简要回顾文献之后，我们为平等和不平等约束的多目标问题给出了适当的扩展拉格朗日定义。我们在一般的计算方案中利用了这个对象，事实证明，在温和的假设下，该方案可以收敛到此类问题的弱Pareto点。然后，我们提供该算法的修改版本，该修改版本更适用于实际实现，并在合理的假设下再次证明了收敛性。最后，计算实验表明，所提出的方法不仅可以在实践中起作用，而且相对于最新方法也具有竞争力。