Metric Subregularity of Subdifferential and KL Property of Exponent 1/2

Shaohua Pan, Dongdong Zhang, Yulan Liu

Published 2018-12-03Version 1

For a proper lower semicontinuous function, we study the relations between the metric subregularity of its limiting subdifferential relative to the critical set and the KL property of exponent 1/2. When the function is convex, we establish the equivalence between them. When the function is nonconvex, we show that the KL property of exponent 1/2 along with the quadratic growth on the critical set implies the metric subregularity of the subdifferential relative to the critical set; and if the function is primal-lower-nice, under an assumption on stationary values, the latter implies the former. These results provide a bridge for the two kinds of regularity and contribute to enriching each other.