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has been cited by the following article:

• TITLE: A Graduated Nonconvex Regularization for Sparse High Dimensional Model Estimation

  AUTHORS: Thomas F. Coleman, Yuying Li

  KEYWORDS: Sparse Model Estimation, Variable Selection lo Regularization

  JOURNAL NAME: Journal of Computer and Communications, Vol.2 No.11, September 12, 2014

  ABSTRACT: Many high dimensional data mining problems can be formulated as minimizing an empirical loss function with a penalty proportional to the number of variables required to describe a model. We propose a graduated non-convexification method to facilitate tracking of a global minimizer of this problem. We prove that under some conditions the proposed regularization problem using the continuous piecewise linear approximation is equivalent to the original lo regularization problem. In addition, a family of graduated nonconvex approximations are proposed to approximate its l1 continuous approximation. Computational results are presented to illustrate the performance.