  The aim of this paper is to design an efficient multigrid method for
constrained convex optimization problems arising from discretization of some
underlying infinite dimensional problems. Due to problem dependency of this
approach, we only consider bound constraints with (possibly) a single equality
constraint. As our aim is to target large-scale problems, we want to avoid
computation of second derivatives of the objective function, thus excluding
Newton like methods. We propose a smoothing operator that only uses first-order
information and study the computational efficiency of the resulting method.
