A Survey of Second-Order Neurodynamic Systems from Optimization Perspective

Over the past two decades, second-order neurodynamic systems have attracted increasing attention due to their strong capability in modeling and solving complex optimization problems. Unlike classical first-order approaches, these continuous neurodynamics exhibit inertial effects, which essentially provide a mechanism for accelerated convergence. We provide an overview of the development of secondorder neurodynamic systems from an optimization perspective. We first introduced the basic theoretical framework of second-order neurodynamic systems, including the continuous-time formulations and their connection to optimization models. The review is divided into two main threads: unconstrained and constrained optimization. Based on this categorization, the representative models and solution strategies are analyzed in detail, covering smooth and nonsmooth, as well as convex and nonconvex optimization problems. Finally, we highlight the limitations of the current study and outline some directions for future research.