Zeroing neural network for optimization: A survey of theory and applications

Zeroing neural network (ZNN) provides a dynamical-systems approach for solving time-varying optimization problems. This survey revisits ZNN from an optimization-oriented perspective. First, recent advances in ZNN are reviewed, including error construction, convergence mechanisms, robustness enhancement, and the relationship between continuous-time models and their discrete-time counterparts. These developments clarify the theoretical foundations underlying the use of error-driven dynamics for tracking time-varying solutions. Next, the survey explains how representative linear and nonlinear optimization problems can be embedded into the ZNN framework. Applications in imaging, signal processing, and robotic control further demonstrate that once inverse problems, estimation tasks, or constrained motion planning problems are formulated as optimization problems, they can be naturally integrated into the ZNN paradigm for real-time computation. Finally, the survey discusses current limitations, emerging opportunities, and future challenges for ZNN in evolving research directions. Overall, ZNN provides a unified and robust pathway linking optimization modeling with real-time dynamic computation across diverse time-varying engineering applications.