# Coordinate Descent for MCP/SCAD Penalized Least Squares Converges Linearly

arXiv: https://arxiv.org/abs/2109.08850 · HTML: https://mlsanity.com/paper/2109.08850/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 1 of its 22 references that are in the map.
- First posted on arXiv 18 Sep 2021.

## Builds on (most cited first, 1 of 1)

- [Calculus of the exponent of Kurdyka-Lojasiewicz inequality and its applications to linear convergence of first-order methods](https://mlsanity.com/paper/1602.02915/) (2016)

## Abstract (arXiv)

Recovering sparse signals from observed data is an important topic in signal/imaging processing, statistics and machine learning. Nonconvex penalized least squares have been attracted a lot of attentions since they enjoy nice statistical properties. Computationally, coordinate descent (CD) is a workhorse for minimizing the nonconvex penalized least squares criterion due to its simplicity and scalability. In this work, we prove the linear convergence rate to CD for solving MCP/SCAD penalized least squares problems.