Dynamic Inertial Newton (DIN) systems have been utilized to inspire and explain a variety of accelerated algorithms for solving diverse optimization problems. In this presentation, we introduce novel algorithms derived from DIN and provide a rigorous convergence analysis. Additionally, we explore their applications through a smoothing approximation approach. Our study is driven by two key objectives: first, to offer a direct method for identifying critical points of objective functions; and second, to address a broad spectrum of real world application challenges, where objective functions are often non-smooth and non-convex.
