@article{5b9db7cd14424e0990e718665facb05b,
title = "A Sparse Semismooth Newton Based Proximal Majorization-Minimization Algorithm for Nonconvex Square-Root-Loss Regression Problems",
abstract = "In this paper, we consider high-dimensional nonconvex square-root-loss regression problems and introduce a proximal majorization-minimization (PMM) algorithm for solving 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.",
keywords = "Nonconvex square-root regression problems, Proximal majorization-minimization, Semismooth Newton method",
author = "Peipei Tang and Chengjing Wang and Defeng Sun and Toh, {Kim Chuan}",
note = "Funding Information: The work of Peipei Tang is supported by the Natural Science Foundation of Zhejiang Province of China under Grant No. LY19A010028 and the Zhejiang Science and Technology Plan Project of China (No. 2020C03091, No. 2021C01164). The work of Defeng Sun is supported by Hong Kong Research Grant Council under Grant PolyU 153014/18P and Shenzhen Research Institute of Big Data, Shenzhen 518000 under Grant 2019ORF01002. The work of Kim-Chuan Toh is supported in part by the Academic Research Fund of the Ministry of Education of Singapore under Grant No. R-146-000-257-112. Part of this research was done while Kim-Chuan Toh was visiting the Shenzhen Research Institute of Big Data at the Chinese University of Hong Kong at Shenzhen. Publisher Copyright: {\textcopyright} 2020 Peipei Tang, Chengjing Wang, Defeng Sun and Kim-Chuan Toh. License: CC-BY 4.0, see https://creativecommons.org/licenses/by/4.0/. Attribution requirements are provided at http://jmlr.org/papers/v21/19-247.html.",
year = "2020",
month = dec,
language = "English",
volume = "21",
pages = "1--38",
journal = "Journal of Machine Learning Research",
issn = "1532-4435",
publisher = "Microtome Publishing",
}