An unconstrained \(\ell_q\) minimization with \(0<q\leq 1\) for sparse solution of underdetermined linear systems. (English) Zbl 1220.65051
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.
Reviewer: Constantin Popa (Constanţa)
MSC:
65F22 | Ill-posedness and regularization problems in numerical linear algebra |
65F50 | Computational methods for sparse matrices |
65F10 | Iterative numerical methods for linear systems |