In this paper, we consider multi-objective optimization problems with a sparsity constraint on the vector of variables. For this class of problems, inspired by the homonymous necessary optimality condition for sparse single-objective optimization, we define the concept of L-stationarity and we analyze its relationships with other existing conditions and Pareto optimality concepts. We then propose two novel algorithmic approaches: the first one is an iterative hard thresholding method aiming to find a single L-stationary solution, while the second one is a two-stage algorithm designed to construct an approximation of the whole Pareto front. Both methods are characterized by theoretical properties of convergence to points satisfying necessary conditions for Pareto optimality. Moreover, we report numerical results establishing the practical effectiveness of the proposed methodologies.

在本文中，我们考虑对变量向量具有稀疏约束的多目标优化问题。对于此类问题，受稀疏单目标优化的同名必要最优条件的启发，我们定义了L-平稳性的概念，并分析了它与其他现有条件和帕累托最优概念的关系。然后，我们提出了两种新颖的算法方法：第一种是迭代硬阈值方法，旨在找到单个L平稳解，而第二种是两阶段算法，旨在构造整个 Pareto 前沿的近似值。这两种方法的特点都是收敛于满足帕累托最优性必要条件的点的理论特性。此外，我们报告了数值结果，证明了所提出的方法的实际有效性。