An upper estimate for the Clarke subdifferential of an infimal value function proved via the Mordukhovich subdifferential

The aim of this note is to give an alternative proof for a recent result due to Dorsch et al., which provides an upper estimate for the Clarke subdifferential of an infimal value function. We show the validity of this result under a weaker condition than the one assumed in the aforementioned paper, while the use of the Mordukhovich subdifferential, as an intermediate step, will considerably shorten its proof.