  We extend the approach in [Ann. Statist. 38 (2010) 2499-2524] for identifying
locally optimal designs for nonlinear models. Conceptually the extension is
relatively simple, but the consequences in terms of applications are profound.
As we will demonstrate, we can obtain results for locally optimal designs under
many optimality criteria and for a larger class of models than has been done
hitherto. In many cases the results lead to optimal designs with the minimal
number of support points.
