Quadratic Growth and Strong Metric Subregularity of the Subdifferential for a Class of Non-prox-regular Functions

This paper mainly studies the quadratic growth and strong metric subregularity of subdifferential a function that can be represented as sum twice differentiable in extended sense subdifferentially continuous, prox-regular, epi-differentiable function. For such function, which is not necessarily it shown growth, at local minimizer, positive definiteness subgradient graphical derivative stationary point are equivalent. In addition, other characterizations also given. Besides, properties functions examined.