The authors consider a regularized version of the unconstrained \(\ell_q\) minimization problem, of the form \(\min_{x \in {\mathcal R}^N} \| x \|_{q, \epsilon} + \frac{1}{2 \lambda} \| Ax-b \|^2_2\), where \(0 < q \leq 1\), \(\epsilon > 0\), \(\lambda > 0\). They derive an iterative algorithm to compute a critical point \(x^{\epsilon, q}\) and prove its convergence for any starting point.