  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.
