FT-GPNN: A finite-time convergence solution for multi-set constrained optimization

Abstract

Gradient Neural Networks (GNNs) have demonstrated remarkable progress in handling optimization problems. However, applying GNNs to multi-constrained optimization problems, particularly those with those involving multi-set constraints, poses several challenges. These challenges arise from the complexity of the derivations and the increasing number of constraints. As the number of constraints increases, the optimization problem becomes more complex, making it more challenging for GNN-based methods to effectively identify the optimal solution. Motivated by these challenges, the Finite-Time Gradient Projection Neural Network (FT-GPNN) is introduced for tackling Multi-set Constrained Optimization (MCO). This innovative solution incorporates an Enhanced Sign-Bi-Power (ESBP) activation function and simplifies the design tailored explicitly for MCO. Furthermore, within the Lyapunov stability framework, the theoretical foundation of this model is strengthened by rigorous proof of local convergence. Building upon this foundation, we further establish that our model can achieve convergence within a finite time. To validate the effectiveness of our approach, we present empirical results from numerical experiments conducted under consistent conditions. Notably, our experiments demonstrate that the model using the ESBP activation function outperforms others in terms of finite-time convergence.