Before revision:  Finally, we test the new method for some problems with deficient rank matrices, and compare it with other  popular interior-point methods such as the path-following method (the subroutine pathfollow.m coded by M.~C. Ferris \mbox{%DIFAUXCMD \cite{Gonzaga1992,FMW2007}\hspace{0pt}%DIFAUXCMD ) and Mehrotra's predictor-corrector algorithm (}  the built-in subroutine linprog.m of the MATLAB environment , which was implemented by S. Mehrotra and Y. Zhang \mbox{%DIFAUXCMD \cite{MATLAB,Mehrotra1992,Zhang1998}\hspace{0pt}%DIFAUXCMD ). }  Numerical results show that the new method is more robust than those methods for the large-scale deficient-rank problems without sacrificing its computational efficiency .
After revision:  Finally, we test the new method for some problems with deficient rank matrices, and compare it with other popular interior-point methods such as the path-following method (the subroutine pathfollow.m }\hspace{0pt}%DIFAUXCMD ) and Mehrotra's predictor-corrector algorithm (} the built-in subroutine linprog.m of the MATLAB environment , which was implemented by S. Mehrotra and Y. Zhang \mbox{%DIFAUXCMD \cite{MATLAB,Mehrotra1992,Zhang1998}\hspace{0pt}%DIFAUXCMD ). } Numerical results show that the new method is more robust than those methods for the large-scale deficient-rank problems without sacrificing its computational efficiency .