Subdifferentials of perturbed distance functions in Banach spaces

摘要

In general Banach space setting, we study the perturbed distance function d_S~J (?) determined by a closed subset S and a lower semicontinuous function J(?). In particular, we show that the Frechet subdifferential and the proximal subdifferential of a perturbed distance function are representable by virtue of corresponding normal cones of 5 and subdifferentials of J(?).