  We develop a general theory of convex duality for certain singular control
problems, taking the abstract results by Kramkov and Schachermayer (1999) for
optimal expected utility from nonnegative random variables to the level of
optimal expected utility from increasing, adapted controls. The main
contributions are the formulation of a suitable duality framework, the
identification of the problem's dual functional as well as the full duality for
the primal and dual value functions and their optimizers. The scope of our
results is illustrated by an irreversible investment problem and the
Hindy-Huang-Kreps utility maximization problem for incomplete financial
markets.
