ADMM for least square problems with pairwise-difference penalties for coefficient grouping

Soohee Park, Seung Jun Shin

Research output: Contribution to journalArticlepeer-review


In the era of bigdata, scalability is a crucial issue in learning models. Among many others, the Alternating Direction of Multipliers (ADMM, Boyd et al., 2011) algorithm has gained great popularity in solving large-scale problems efficiently. In this article, we propose applying the ADMM algorithm to solve the least square problem penalized by the pairwise-difference penalty, frequently used to identify group structures among coefficients. ADMM algorithm enables us to solve the high-dimensional problem efficiently in a unified fashion and thus allows us to employ several different types of penalty functions such as LASSO, Elastic Net, SCAD, and MCP for the penalized problem. Additionally, the ADMM algorithm naturally extends the algorithm to distributed computation and real-time updates, both desirable when dealing with large amounts of data.

Original languageEnglish
Pages (from-to)441-451
Number of pages11
JournalCommunications for Statistical Applications and Methods
Issue number4
Publication statusPublished - 2022

Bibliographical note

Funding Information:
This work is partially funded by the National Research Foundation of Korea (NRF) grants 2018R1D1A1B07043034 and 2019R1A4A1028134. 1Corresponding author: Department of Statistics, Korea University, 145 Anam-Ro, Sungbuk-Gu, Seoul 02841, Korea. E-mail:

Publisher Copyright:
© 2022. The Korean Statistical Society, and Korean International Statistical Society. All rights reserved.


  • Alternating direction of multipliers
  • Grouping coefficients
  • High-dimensional data
  • Real-time update

ASJC Scopus subject areas

  • Statistics and Probability
  • Modelling and Simulation
  • Finance
  • Statistics, Probability and Uncertainty
  • Applied Mathematics


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