A Projection Neural Network for the Generalized Lasso

Majid Mohammadi

Research output: Contribution to journalArticleScientificpeer-review


The generalized lasso (GLasso) is an extension of the lasso regression in which there is an l_{1} penalty term (or regularization) of the linearly transformed coefficient vector. Finding the optimal solution of GLasso is not straightforward since the penalty term is not differentiable. This brief presents a novel one-layer neural network to solve the generalized lasso for a wide range of penalty transformation matrices. The proposed neural network is proven to be stable in the sense of Lyapunov and converges globally to the optimal solution of the GLasso. It is also shown that the proposed neural solution can solve many optimization problems, including sparse and weighted sparse representations, (weighted) total variation denoising, fused lasso signal approximator, and trend filtering. Disparate experiments on the above problems illustrate and confirm the excellent performance of the proposed neural network in comparison to other competing techniques.

Original languageEnglish
Article number8790992
Pages (from-to)2217-2221
Number of pages5
JournalIEEE Transactions on Neural Networks and Learning Systems
Issue number6
Publication statusPublished - 2020


  • Generalized lasso (GLasso)
  • global convergence
  • Lyapunov
  • neural network

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