An Accelerated Augmented Gradient Neural Network for Constrained Time-Varying Nonlinear Optimization.

Abstract

The constrained time-varying nonlinear optimization (CTVNO) problems with the linear equality and inequality constraints have attracted increasing attention in recent years. Although some models have been developed to address these problems, they still suffer from two critical limitations: complex model architecture and slow transient response. These issues restrict their practical application in engineering. To overcome these drawbacks, an accelerated augmented gradient neural network (AAGNN) is proposed. By integrating the error function with energy function gradients, the AAGNN efficiently exploits the essential information of the original problem, thereby reducing the complexity and accelerating convergence. The theoretical analysis demonstrates that the proposed AAGNN excels in achieving high-precision solutions. This stems from its ability to rapidly eliminate large errors through the exponential convergence. Comparative numerical experiments across four benchmarks demonstrate that the AAGNN consistently achieves a lower residual error and faster convergence than existing models. Furthermore, application tests through robotic manipulator trajectory tracking control and portfolio selection of marketed securities confirm the model's superior practical applicability in real-world scenarios.