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The iteratively reweighted l1 algorithm is a widely used method for solvingvarious regularization problems, which generally minimize a differentiable lossfunction combined with a nonconvex regularizer to induce sparsity in thesolution. However, the convergence and the complexity of iteratively reweightedl1 algorithms is generally difficult to analyze, especially for non-Lipschitzdifferentiable regularizers such as nonconvex lp norm regularization. In thispaper, we propose, analyze and test a reweighted l1 algorithm combined with theextrapolation technique under the assumption of Kurdyka-Lojasiewicz (KL)property on the objective. Unlike existing iteratively reweighted l1 algorithmswith extrapolation, our method does not require the Lipschitz differentiabilityon the regularizers nor the smoothing parameters in the weights bounded awayfrom zero. We show the proposed algorithm converges uniquely to a stationarypoint of the regularization problem and has local linear complexity--a muchstronger result than existing ones. Our numerical experiments show theefficiency of our proposed method.

An Extrapolated Iteratively Reweighted l1 Method with Complexity Analysis