References
- F. Alizadeh (1991). Combinatorial Optimization with Interior-point Methods and Semi-definite Matrices. Ph.D. thesis. Computer Sience Department, University of Minnesota, Minneapolis, MN, USA.
- S. Browne, J. Dongarra, E. Grosse, and T. Rowan (1995). The NETLIB mathematical software repository. Corporation for National Research Initiatives.
- J. Faraut and A. Korányi (1994). Analysis on Symmetric Cone. Oxford University Press, New York, New York.
- L. Faybusovich (1997). Linear systems in Jordan algebras and primal-dual interior-point algorithms. J. Comput. Appl. Math. 86:149–175.
- Z. Gongyun and J. Sun (1999). On the rate of local convergence of high-order-infeasible-path-following algorithms for P*-linear complementarity problems. Comput. Optim. Appl. 14:293–307.
- G. Gu, M. Zangiabadi, and C. Roos (2011). Full Nesterov-Todd step infeasible interior-point method for symmetric optimization. Eur. J. Oper. Res. 214:473–484.
- O. Güler (1996). Barrier functions in interior-point methods. Math. Oper. Res. 21:860–885.
- P. Hung and Y. Ye (1996). An asymptotical -iteration path-following linear programming algorithm that use wide neighborhoods. SIAM J. Optim. 6:570–586.
- B. Jansen, C. Roos, T. Terlaky, and Y. Ye (1996). Improved complexity using higher-order correctors for primal-dual Dikin affine scaling. Math. Program. 76:117–130.
- N. Karmarkar (1984). A new polynomial-time algorithm for linear programming. Combinatorica 4:373–393.
- H. Lahmam, J. M. Cadou, H. Zahrouni, N. Damil, and M. Potier-Ferry (2002). High-order predictor-corrector algorithms. Int. nJ. Numer. Meth. Engin. 55:685–704.
- C. Liu (2012). Study on complexity of some interior-point algorithms in conic programming (in Chinese). Ph.D. thesis, Xidian University, Xi'an, China.
- H. Liu, X. Yang, and C. Liu (2013). A new wide neighborhood primal-dual infeasible-interior-point method for symmetric cone programming. J. Optim. Theory Appl. 158: 796–815.
- S. Mehrotra (1992). On the implementation of a primal-dual interior point method. SIAM J. Optim. 2:575–601.
- Y. Nesterov and A. Nemirovskii (1994). Interior Point Polynomial Algorithms in Convex Programming. Vol. 13. Society for Industrial and Applied Mathematics, Philadelphia, PA.
- Y. Nesterov and M. Todd (1997). Self-scaled barriers and interior-point methods for convex programming. Math. Oper. Res. 22:1–42.
- Y. Nesterov and M. Todd (1998). Primal-dual interior-point methods for self-scaled cones. SIAM J. Optim. 8:324–364.
- B. Rangarajan (2006). Polynomial convergence of infeasible-interior-point methods over symmetric cones. SIAM J. Optim. 16:1211–1229.
- M. Salahi and N. Mahdavi-Amiri (2006). Polynomial time second order Mehrotra-type predictor-corrector algorithms. Appl. Math. Comput. 183:646–658.
- S. Schmieta and F. Alizadeh (2003). Extension of primal-dual interior point algorithm to symmetric cones. Math. Program. 96:409–438.
- J. Stoer (2001). High order long-step methods for solving linear complementarity problems. Ann. Oper. Res. 103:149–159.
- M. Todd, K. Toh, and R. Tütüncü (1998). On the Nesterov-Todd direction in semidefinite programming. SIAM J. Optim. 8:769–796.
- G. Wang and Y. Bai (2012). A new full Nesterov-Todd step primal-dual path following interior-point algorithm for symmetric optimization. J. Optim. Theory Appl. 154:966–985.
- G. Wang, C. Yu, and K. Teo (2013). A new full Nesterov-Todd step feasible interior-point method for convex quadratic optimization over symmetric cone. App. Math. Comput. 221:329–343.
- G. Wang, L. Kong, T. Tao, and G. Lesaja (2015). Improved complexity analysis of full Nesterov-Todd step feasible interior-point method for symmetric optimization. J. Optim. Theory Appl. 166:588–604.
- J. Zhang and K. Zhang (2011). Polynomial complexity of an interior point algorithm with a second order corrector step for symmetric cone programming. Math. Meth. Oper. Res. 73: 75–90.
- Y. Zhang and D. Zhang (1995). On polynomial of the Mehrotra-type predictor-corrector interior-point algorithms. Math. Program. 68:303–318.