Journal
COMPUTATIONAL STATISTICS & DATA ANALYSIS
Volume 94, Issue -, Pages 275-286Publisher
ELSEVIER
DOI: 10.1016/j.csda.2015.08.019
Keywords
Local quadratic approximation; l(1)-penalization; Nonconvex penalization; LASSO; SCAD; MCP
Funding
- National Research Foundation of Korea (NRF) grant - Korea government (MSIP) [2014R1A2A2A01004496]
- National Research Foundation of Korea (NRF) - Ministry of Science, ICT. & Future Planning [2014R1A1A1002995]
- National Research Foundation of Korea [2014R1A1A1002995, 2014R1A2A2A01004496] Funding Source: Korea Institute of Science & Technology Information (KISTI), National Science & Technology Information Service (NTIS)
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In this paper, we propose an optimization algorithm called the modified local quadratic approximation algorithm for minimizing various l(1)-penalized convex loss functions. The proposed algorithm iteratively solves l(1)-penalized local quadratic approximations of the loss function, and then modifies the solution whenever it fails to decrease the original l(1)-penalized loss function. As an extension, we construct an algorithm for minimizing various nonconvex penalized convex loss functions by combining the proposed algorithm and convex concave procedure, which can be applied to most nonconvex penalty functions such as the smoothly clipped absolute deviation and minimax concave penalty functions. Numerical studies show that the algorithm is stable and fast for solving high dimensional penalized optimization problems. (C) 2015 Elsevier B.V. All rights reserved.
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