# square-root-PMM

#### square-root-PMM version 1.0: a MATLAB software for square-root regression problems Peipei Tang, Chengjing Wang, Defeng Sun, and Kim-Chuan Toh

This is software package for solving the square-root regression problem:
$$\min_\beta \{ \|X\beta -b\|_{2}+\lambda p(\beta)-q(\beta)\}.$$
A sparse semismooth Newton based proximal majorization-minimization algorithm is used to solve this problem; details can be found in the following reference.

• Peipei Tang, Chengjing Wang, Defeng Sun, and Kim-Chuan Toh,
A Sparse Semismooth Newton Based Proximal Majorization-Minimization Algorithm for Nonconvex Square-Root-Loss Regression Problems, Journal of Machine Learning Research 21(226):1–38, 2020.
• Codes available at Github.