A smoothing approximation approach to dynamical inertial newton systems for non-smooth and non-convex optimization: the deterministic case
Ouayl Chadli, Xin Li, R. N. Mohapatra, Jen-Chih Yao · Optimization · 2025
Dynamical systems have inspired and explained several accelerated algorithms for a wide range of optimization problems. But due to the lack of smoothness and convexity of the objective functions in many real world applications, we cannot directly apply these accelerated algorithms in these situations. This paper proposes to apply a smoothing approximation approach to address non-smooth, non-convex machine learning optimization problems. Our work is motivated by the following goal: developing a direct method for finding critical points of objective functions of machine learning problems where functions are known to be non-smooth and non-convex. To achieve these goals, we establish the convergence of an alternative algorithm for smooth functions without convexity that supplements some recent results of Attouch et al.