Simplified Gradient-Zeroing Neuronet for Temporally-Variant Convex Objective Function Minimization

Solving temporally-variant problems has recently become an important topic in the fields of science and engineering. With the development of artificial intelligence, gradient neuronet (GN) and zeroing neuronet (ZN) have been successively proposed to solve temporally-variant problems. GN has the advantage of fast convergence, while ZN excels in precision. In addition, gradient-zeroing neuronet (GZN) has been proposed, providing a new solution for temporally-variant problems. In this paper, we solve the temporally-variant convex objective function minimization, and introduce a simplified gradient-zeroing neuronet (SGZN). To meet the requirements of digital hardware devices, we discretize the SGZN model by the explicit linear three-step formula, resulting in the discrete SGZN algorithm. Finally, we conduct numerical experiments to validate that the SGZN shares the same characteristics as GZN, exhibiting both fast convergence and high precision, with simplified complexity.