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 -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 -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 -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 -LPNN algorithm with both the LASSO-LPNN model and a standard digital method.

中文翻译：

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基于 LPNN 的 LASSO 问题方法，通过一系列正则化最小化

在压缩采样理论中，最小绝对收缩和选择算子（LASSO）是一个有代表性的问题。然而，不可微的约束阻碍了拉格朗日编程神经网络 (LPNN) 的使用。我们在本文中介绍了-LPNN 模型，这是一种解决 LASSO 最小化以及基础理论支持的新算法。首先，我们设计了一系列平滑约束优化问题，通过引入一个方便的可微近似于不可微的范数约束。接下来，我们证明正则化中间问题的最优解收敛到 LASSO 的最优稀疏信号。然后，对于序列中的每个正则化问题，-LPNN动力学模型推导出来，并建立了其平衡状态的渐近稳定性。最后，进行数值模拟以比较所提出的-LPNN 算法与 LASSO-LPNN 模型和标准数字方法的性能。