A note on application of nesterov’s method in solving lasso-type problems

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Original languageEnglish
Article numberA002
Pages (from-to)1673-1682
Journal / PublicationCommunications in Statistics: Simulation and Computation
Issue number7
Publication statusPublished - 1 Jan 2015
Externally publishedYes


Many different algorithms have been proposed to solve penalized variable selection problems, in particular lasso and its variants, including group lasso and fused lasso. Loss functions other than quadratic loss also pose significant challenges for finding efficient solvers. Here, we note that Nesterov’s method can be used to transform an optimization problem with general smooth convex loss to quadratic loss with identity covariate matrix in each iteration. After such reduction, the problem becomes much easier to solve or even can be solved in closed form in some cases. We perform some simulations and apply our implementation to phoneme discrimination.

Research Area(s)

  • Coordinate descent, Fused lasso, Group lasso, Lasso