Sparse pseudoinverses via LP and SDP relaxations of Moore-Penrose
  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. 
Victor K. Fuentes, Marcia Fampa, Jon Lee
math.NA