  The iteratively reweighted l1 algorithm is a widely used method for solving
various regularization problems, which generally minimize a differentiable loss
function combined with a nonconvex regularizer to induce sparsity in the
solution. However, the convergence and the complexity of iteratively reweighted
l1 algorithms is generally difficult to analyze, especially for non-Lipschitz
differentiable regularizers such as nonconvex lp norm regularization. In this
paper, we propose, analyze and test a reweighted l1 algorithm combined with the
extrapolation technique under the assumption of Kurdyka-Lojasiewicz (KL)
property on the objective. Unlike existing iteratively reweighted l1 algorithms
with extrapolation, our method does not require the Lipschitz differentiability
on the regularizers nor the smoothing parameters in the weights bounded away
from zero. We show the proposed algorithm converges uniquely to a stationary
point of the regularization problem and has local linear complexity--a much
stronger result than existing ones. Our numerical experiments show the
efficiency of our proposed method.
