The main result of this paper is that $g$-inverses are not needed for computing optimum designs when the singularity of the information matrix is unavoidable. They are, of course, needed for the analysis. It will be shown that it is possible to augment the experimental region so that procedures for computing optimum designs for $s$ out $k$ parameters $(s < k)$ which are developed for the nonsingular case may also be used for the singular case.
"Computation of the Optimum Designs Under Singular Information Matrices." Ann. Statist. 6 (2) 465 - 467, March, 1978. https://doi.org/10.1214/aos/1176344137