王承竞 副教授
  • 学历:博士研究生毕业
  • 学位:理学博士学位
  • 办公地点:西南交通大学数学学院
  • 毕业院校:新加坡国立大学
  • 所在单位:数学学院
论文成果
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  • 发表刊物:Journal of Scientific Computing
  • 关键字:Sparse group square-root Lasso; Semismooth Newton method; Augmented Lagrangian method
  • 摘要:Square-root Lasso problems have already be shown to be robust regression problems. Furthermore, square-root regression problems with structured sparsity also plays an important role in statistics and machine learning. In this paper, we focus on the numerical computation of large-scale linearly constrained sparse group square-root Lasso problems. In order to overcome the difficulty that there are two nonsmooth terms in the objective function, we propose a dual semismooth Newton (SSN) based augmented Lagrangian method (ALM) for it. That is, we apply the ALM to the dual problem with the subproblem solved by the SSN method. To apply the SSN method, the positive definiteness of the generalized Jacobian is very important. Hence we characterize the equivalence of its positive definiteness and the constraint nondegeneracy condition of the corresponding primal problem. In numerical implementation, we fully employ the second order sparsity so that the Newton direction can be efficiently obtained. Numerical experiments demonstrate the efficiency of the proposed algorithm.
  • 第一作者:Chengjing Wang, Peipei Tang
  • 论文类型:SCI
  • 卷号:96
  • 是否译文:
  • 发表时间:2023-01-09
  • 收录刊物:SCI
  • 附件: Published_version_sparse group square-root Lasso problems.pdf

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