A novel representation of rank constraints for non-square real matrices
  We present a novel representation of rank constraints for non-square real matrices. We establish relationships with some existing results, which are particular cases of our representation. One of these particular cases, is a representation of the $\ell_0$ pseudo-norm, which is used in sparse representation problems. Finally, we describe how our representation can be included in rank-constrained optimization and in rank-minimization problems. 
Ram\'on A. Delgado, Juan C. Ag\"uero and Graham C. Goodwin
math.OC