This talk investigates the properties of Sharpness-Aware Minimization (SAM), a recently proposed gradient-based optimization method (Foret et al., 2021) that significantly enhances the generalization of deep neural networks by seeking parameters in neighborhoods with uniformly low loss. The convergence properties, including the stationarity of accumulation points, the convergence of the gradient sequence to the origin, the function value sequence to the optimal value, and the iterate sequence to the optimal solution, are established for this method. The universality of the proposed convergence analysis, based on inexact gradient descent frameworks, allows its extension to all normalized variants of SAM.