  Pseudoinverses are ubiquitous tools for handling over- and under-determined
systems of equations. For computational efficiency, sparse pseudoinverses are
desirable. Recently, sparse left and right pseudoinverses were introduced,
using 1-norm minimization and linear programming. We introduce several new
sparse pseudoinverses by developing linear and semi-definite programming
relaxations of the well-known Moore-Penrose properties.
