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arXiv · 1408.0578

A Cyclic Coordinate Descent Algorithm for lq Regularization

Jinshan Zeng·Zhimin Peng·Shaobo Lin·Zongben Xu
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Abstract

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.

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Jinshan Zeng, Zhimin Peng, Shaobo Lin, Zongben Xu. 2014-08-04. A Cyclic Coordinate Descent Algorithm for lq Regularization. https://arxiv.org/abs/1408.0578

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