A generalized elastic net regularization with smoothed $$ell _{q}$$ penalty for sparse vector recovery

In this paper, we propose an iterative algorithm for solving the generalized elastic net regularization problem with smoothed (ell _{q} (0 penalty for recovering sparse vectors. We prove the convergence result of the algorithm based on the algebraic method. Under certain conditions, we show that the iterative solutions converge to a local minimizer of the generalized elastic net regularization problem and we also present an error bound. Theoretical analysis and numerical results show that the proposed algorithm is promising.