Reviews: Convergence of Cubic Regularization for Nonconvex Optimization under KL Property

The paper investigates the convergence of different measurement of cubic regularization method for non-convex optimization under KL property. It consists with a list of work on CR methods based on the analysis of Nesterove el.s' work. Since the type of methods can guarantee the convergence to the second-order stationary point, it is quite popular also considering the raising of training neural networks. The paper is well-written, clear-organized and the theorems and proofs are easy to follow. Note that this is a pure theoretical work i.e., without new algorithms and/or numerical experiments.