# A Cyclic Coordinate Descent Algorithm for lq Regularization

arXiv: https://arxiv.org/abs/1408.0578 · HTML: https://mlsanity.com/paper/1408.0578/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Aug 2014.

## Built on by (most cited first, 1 of 1)

- [Cyclic Block Coordinate Descent With Variance Reduction for Composite Nonconvex Optimization](https://mlsanity.com/paper/2212.05088/) (2022)

## Abstract (arXiv)

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.