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LPNN‐based approach for LASSO problem via a sequence of regularized minimizations
Author(s) -
Zeglaoui Anis,
Houmia Anouar,
Mejai Maher,
Aloui Radhouane
Publication year - 2021
Publication title -
international journal of adaptive control and signal processing
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.73
H-Index - 66
eISSN - 1099-1115
pISSN - 0890-6327
DOI - 10.1002/acs.3303
Subject(s) - lasso (programming language) , differentiable function , mathematical optimization , sequence (biology) , constraint (computer aided design) , compressed sensing , regularization (linguistics) , mathematics , minification , norm (philosophy) , algorithm , computer science , artificial intelligence , biology , world wide web , genetics , mathematical analysis , geometry , political science , law
Summary In compressive sampling theory, the least absolute shrinkage and selection operator (LASSO) is a representative problem. Nevertheless, the non‐differentiable constraint impedes the use of Lagrange programming neural networks (LPNNs). We present in this article the k‐LPNN model, a novel algorithm that tackles the LASSO minimization together with the underlying theory support. First, we design a sequence of smooth constrained optimization problems, by introducing a convenient differentiable approximation to the non‐differentiablel 1‐norm constraint. Next, we prove that the optimal solutions of the regularized intermediate problems converge to the optimal sparse signal for the LASSO. Then, for every regularized problem from the sequence, the k‐LPNN dynamic model is derived, and the asymptotic stability of its equilibrium state is established as well. Finally, numerical simulations are carried out to compare the performance of the proposed k‐LPNN algorithm with both the LASSO‐LPNN model and a standard digital method.