A Cyclic Coordinate Descent Algorithm for lq Regularization

In recent studies on sparse modeling, lq (0<q<1) regularization has received considerable attention due to its superiorities on sparsity-inducing and bias reduction over the l1 regularization.In this paper, we propose a cyclic coordinate descent (CCD) algorithm for lq regularization. Our main result states that the CCD algorithm converges globally to a stationary point as long as the stepsize is less than a positive constant. Furthermore, we demonstrate that the CCD algorithm converges to a local minimizer under certain additional conditions. Our numerical experiments demonstrate the efficiency of the CCD algorithm.