An Alternating Direction Method of Multipliers for MCP-penalized Regression with High-dimensional Data

作者：Shi, Yue Yong; Jiao, Yu Ling; Cao, Yong Xiu; Liu, Yan Yan^*

来源：Acta Mathematica Sinica-English Series, 2018, 34(12): 1892-1906.

DOI：10.1007/s10114-018-7096-8

• Alternating direction method of multipliers
• coordinate descent
• continuation
• high-dimensional BIC
• minimax concave penalty
• penalized least squares

The minimax concave penalty (MCP) has been demonstrated theoretically and practically to be effective in nonconvex penalization for variable selection and parameter estimation. In this paper, we develop an efficient alternating direction method of multipliers (ADMM) with continuation algorithm for solving the MCP-penalized least squares problem in high dimensions. Under some mild conditions, we study the convergence properties and the Karush-Kuhn-Tucker (KKT) optimality conditions of the proposed method. A high-dimensional BIC is developed to select the optimal tuning parameters. Simulations and a real data example are presented to illustrate the efficiency and accuracy of the proposed method.

• 出版日期2018-12
• 单位武汉大学; 中国地质大学（北京）; 中南财经政法大学