A Cyclic Coordinate Descent Algorithm for lq Regularization
  In recent studies on sparse modeling, $l_q$ ($0<q<1$) regularization has received considerable attention due to its superiorities on sparsity-inducing and bias reduction over the $l_1$ regularization.In this paper, we propose a cyclic coordinate descent (CCD) algorithm for $l_q$ 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. 
Jinshan Zeng, Zhimin Peng, Shaobo Lin, and Zongben Xu
math.OC