Adaptive gradient-aware neural dynamics: Towards fast and accurate solutions for dynamic convex optimization

Constrained Dynamic Convex Optimization (CDCO) represents a core challenge in many engineering applications, where the objective is to minimize a time-varying cost function subject to dynamically evolving constraints. While recent neural network-based methods have demonstrated potential in addressing CDCO, they still suffer from limitations in convergence and solution accuracy, which restrict their effectiveness in real-world deployments. To overcome these challenges, we propose an Adaptive Gradient-Aware Neural Dynamics (AGAND). As an artificial intelligence model derived from a branch of Hopfield networks, AGAND integrates a gradient-aware term with a time derivative term to enhance solution performance. Our AGAND uses gradient information and time-derivative data to achieve faster and more accurate solutions for CDCO. Besides, the convergence of the model is further boosted by introducing state-aware coefficient with gradient feedback mechanism. Theoretical analysis demonstrates the global convergence of the AGAND, along with a detailed complexity assessment. To further adapt AGAND for practical deployment, a discretization scheme is proposed to facilitate implementation on digital hardware. Comparative experiments with state-of-the-art methods illustrate the competitiveness of our AGAND in terms of convergence and accuracy, achieving Average Steady-state Residual Error (ASSRE) of $3.10\times 10^{-3}$ and Convergence Time (CT) of 0.04 s. Finally, a robot kinematics scheme and hyperspectral image target detection are formulated on the basis of our AGAND, demonstrating the feasibility and practical utility of the AGAND in real-world engineering problems.