  This paper concerns the projected gradient descent (PGD) algorithm for the
problem of minimizing a continuously differentiable function on a nonempty
closed subset of a Euclidean vector space. Without further assumptions, this
problem is intractable and devoted algorithms are only expected to find a
stationary point. PGD is known to generate a sequence whose accumulation points
are Mordukhovich stationary. In this paper, these accumulation points are
proven to be Bouligand stationary, and even proximally stationary if the
gradient is locally Lipschitz continuous. These are the strongest stationarity
properties that can be expected for the considered problem.
