Design and analysis of gradient-based differential neural network for solving time-varying quadratic problems with inequality constraint.

Abstract

The inequality-constrained time-varying quadratic program (IC-TVQP) is a fundamental and challenging problem that arises across various scientific and engineering domains. This work introduces a gradient-differential neural network (GDNN) designed for IC-TVQP problem resolution. Finite-time convergence and enhanced computational efficiency are realized in the GDNN through the implementation of a refined sign-bi-power activation function. Comparative analyses against established approaches, including the conventional gradient-based neural network (CGNN), varying-parameter convergence differential neural network (VP-CDNN), and zeroing neural network (ZNN), highlight the GDNN´s superior solution accuracy, evidenced by significantly lower residual errors. Extensive numerical simulations further validate its effectiveness, particularly demonstrating enhanced robustness to variations in scaling factors. To illustrate its practical utility, we apply the GDNN model to a time-varying financial portfolio optimization problem, showcasing its effectiveness and real-world applicability.