Two Recurrent Neural Networks With Reduced Model Complexity for Constrained l₁-Norm Optimization

Because of the robustness and sparsity performance of least absolute deviation (LAD or
$l_{1}$
) optimization, developing effective solution methods becomes an important topic. Recurrent neural networks (RNNs) are reported to be capable of effectively solving constrained
$l_{1}$
-norm optimization problems, but their convergence speed is limited. To accelerate the convergence, this article introduces two RNNs, in form of continuous- and discrete-time systems, for solving
$l_{1}$
-norm optimization problems with linear equality and inequality constraints. The RNNs are theoretically proven to be globally convergent to optimal solutions without any condition. With reduced model complexity, the two RNNs can significantly expedite constrained
$l_{1}$
-norm optimization. Numerical simulation results show that the two RNNs spend much less computational time than related RNNs and numerical optimization algorithms for linearly constrained
$l_{1}$
-norm optimization.