# A sparse semismooth Newton based proximal majorization-minimization algorithm for nonconvex square-root-loss regression problems

arXiv: https://arxiv.org/abs/1903.11460 · HTML: https://mlsanity.com/paper/1903.11460/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Mar 2019.

## Built on by (most cited first, 3 of 3)

- [Low-Rank Tensor Learning by Generalized Nonconvex Regularization](https://mlsanity.com/paper/2410.18402/) (2024)
- [A proximal-proximal majorization-minimization algorithm for nonconvex tuning-free robust regression problems](https://mlsanity.com/paper/2106.13683/) (2021)
- [Wasserstein Distributionally Robust Optimization Through the Lens of Structural Causal Models and Individual Fairness](https://mlsanity.com/paper/2509.26275/) (2025)

## Abstract (arXiv)

In this paper, we consider high-dimensional nonconvex square-root-loss regression problems and introduce a proximal majorization-minimization (PMM) algorithm for these problems. Our key idea for making the proposed PMM to be efficient is to develop a sparse semismooth Newton method to solve the corresponding subproblems. By using the Kurdyka-Lojasiewicz property exhibited in the underlining problems, we prove that the PMM algorithm converges to a d-stationary point. We also analyze the oracle property of the initial subproblem used in our algorithm. Extensive numerical experiments are presented to demonstrate the high efficiency of the proposed PMM algorithm.