A note on the existence of the Alizadeh-Haeberly-Overton direction for semidefinite programming

F. Alizadeh, J.-P.A. Haeberly and M.L. Overton, Primal-dual interior-point methods for semidefinite programming, Technical Report 659, Computer Science Department, Courant Institute of Mathematical Sciences, New York University (1994).

R.A. Horn and C.R. Johnson,Matrix Analysis (Cambridge University Press, New York, 1985).

R.A. Horn and C.R. Johnson,Topics in Matrix Analysis (Cambridge University Press, New York, 1991).

M. Shida, S. Shindoh and M. Kojima, Existence of search directions in interior-point algorithms for the SDP and monotone SDLCP programs, Research Report #B-310, Dept. of Mathematical and Computing Sciences, Tokyo Institute of Technology, 2-12-1 Oh-Okayama, Meguro-ku, Tokyo 152 (1996).

M.J. Todd, K.C. Toh and R.H. Tütüncü, On the Nesterov-Todd direction in semidefinite programming, Technical Report, School of Operations Research and Industrial Engineering, Cornell University, Ithaca, NY 14853, USA (March 1996).