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- Title
LPNN‐based approach for LASSO problem via a sequence of regularized minimizations.
- Authors
Zeglaoui, Anis; Houmia, Anouar; Mejai, Maher; Aloui, Radhouane
- Abstract
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 𝒫k‐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‐differentiable l1‐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 𝒫k‐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 𝒫k‐LPNN algorithm with both the LASSO‐LPNN model and a standard digital method.
- Subjects
ALGORITHMS; COMPUTER simulation; DYNAMIC models; LYAPUNOV stability; MATHEMATICAL regularization; NONSMOOTH optimization; CONSTRAINED optimization
- Publication
International Journal of Adaptive Control & Signal Processing, 2021, Vol 35, Issue 9, p1842
- ISSN
0890-6327
- Publication type
Article
- DOI
10.1002/acs.3303