Min-min minimization for the fractional ℓ0-regularized problem

In this paper, we present a novel unconstrained fractional ${\ell }_0$ regularization (FL0R) model to solve cardinality minimization. Firstly, we construct an interesting $\min -\min$ minimization from FL0R by introducing a middle variable of sparsity. Then, we prove that the solution to $\min -\min$ minimization with a given sparsity is one of FL0R. Finally, some numerical examples are presented to illustrate the effectiveness and validity of the new model.