The document proposes a two-layer recurrent neural network to solve non-smooth convex optimization problems subject to constraints. It proves that the neural network has a low complexity, reaches the feasible region in finite time, and converges to an equilibrium point that is equivalent to the optimal solution of the original problem. The neural network is then applied to solve nonlinear convex programs with constraints and L1-norm minimization problems.

1. A TWO-LAYER RECURRENT NEURAL NETWORK FOR
NONSMOOTH CONVEX OPTIMIZATION PROBLEMS
ABSTRACT
In this paper, a two-layer recurrent neural network is proposed to solve the non smooth
convex optimization problem subject to convex inequality and linear equality constraints.
Compared with existing neural network models, the proposed neural network has a low model
complexity and avoids penalty parameters. It is proved that from any initial point, the state of the
proposed neural network reaches the equality feasible region in finite time and stays there
thereafter. Moreover, the state is unique if the initial point lies in the equality feasible region.
The equilibrium point set of the proposed neural network is proved to be equivalent to the
Karush–Kuhn–Tucker optimality set of the original optimization problem. It is further proved
that the equilibrium point of the proposed neural network is stable in the sense of Lyapunov.
Moreover, from any initial point, the state is proved to be convergent to an equilibrium point of
the proposed neural network. Finally, as applications, the proposed neural network is used to
solve nonlinear convex programming with linear constraints and L1-norm minimization
problems.