References
- W. Ai and S. Zhang, An O(√nL) iteration primal–dual path-following method, based on wide neighborhoods and large updates, for monotone LCP, SIAM J. Optim. 16 (2005), pp. 400–417 doi: 10.1137/040604492
- F. Alizadeh, Combinatorial optimization with interior-point methods and semi-definite matrices, Ph.D. thesis, Computer Science Department, University of Minnesota, Minneapolis, MN, 1991.
- F. Alizadeh, Interior point methods in semidefinite programming with applications to combinatorial optimization, SIAM J. Optim. 5 (1995), pp. 13–51 doi: 10.1137/0805002
- F. Alizadeh, J. A. Haeberly and M. L. Overton, Primal–dual interior-point methods for semidefinite programming: Convergence rates, stability and numerical results, SIAM J. Optim. 8 (1998), pp. 746–768 doi: 10.1137/S1052623496304700
- S. Boyd, L.E. Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, SIAM, Philadelphia, PA, 1994.
- Z. Feng and L. Fang, A wide neighbourhood interior-point method with iteration-complexity bound for semidefinite programming, Optimization 59 (2010), pp. 1235–1246 doi: 10.1080/02331930903104382
- G. H. Gulub and C. F. Van Loan, Matrix Computations, The Johns Hopkins University Press, Baltimore, MD, 1989
- C. Helmberg, F. Rendl, R. J. Vanderbei and H. Wolkowicz, An interior-point method for semidefinite programming, SIAM J. Optim. 6 (1996), pp. 342–361 doi: 10.1137/0806020
- R. A. Horn and C. R. Johnson, Topics in Matrix Analysis, Cambridge University Press, New York, 1991
- E. D. Klerk, Aspects of Semidefinite Programming: Interior Point Algorithms and Selected Applications, Kluwer Academic Publishers, Dordrecht, 2002
- M. H. Koulaei and T. Terlaky, On the complexity analysis of a Mehrotra-type primal–dual feasible algorithm for semidefinite optimization, Optim. Methods Softw. 25 (2010), pp. 467–485 doi: 10.1080/10556780802571392
- Y. Li and T. Terlaky, A new class of large neighborhood path-following interior point algorithms for semidefinite optimization with iteration complexity, SIAM J. Optim. 20 (2010), pp. 2853–2875 doi: 10.1137/080729311
- C. Liu and H. Liu, A new second-order corrector interior-point algorithm for semidefinite programming, Math. Methods Oper. Res. 75 (2012), pp. 165–183 doi: 10.1007/s00186-012-0379-4
- H. Liu, C. Liu and X. Yang, New complexity analysis of a Mehrotra-type predictor–corrector algorithm for semidefinite programming, Optim. Methods Softw. 1 (2012), pp. 1–16 doi: 10.1080/10556781003796622
- H. Liu, X. Yang and C. Liu, A new wide neighborhood primal–dual infeasible-interior-point method for symmetric cone programming, J. Optim. Theory Appl.2013
- S. Mehrotra, On the implementation of a primal–dual interior point method, SIAM J. Optim. 2 (1992), pp. 575–601 doi: 10.1137/0802028
- R. D.C. Monteiro, Primal–dual path-following algorithms for semidefinite programming, SIAM J. Optim. 7 (1997), pp. 663–678 doi: 10.1137/S1052623495293056
- R. D.C. Monteiro, Polynomial convergence of primal–dual algorithms for semidefinite programming based on Monteiro and Zhang family of directions, SIAM J. Optim. 8 (1998), pp. 797–812 doi: 10.1137/S1052623496308618
- R. D.C. Monteiro and Z. Yin, A unified analysis for a class of long-step primal–dual path-following interior-point algorithms for semidefinite programming, Math. Program. 81 (1998), pp. 281–299
- Y. E. Nesterov and A. Nemirovsky, Interior-Point Methods in Convex Programming: Theory and Applications, SIAM, Philadelphia, PA, 1994
- Y. Nesterov and M. Todd, Self-scaled barriers and interior-point methods for convex programming, Math. Oper. Res. 22 (1997), pp. 1–42 doi: 10.1287/moor.22.1.1
- Y. Nesterov and M. Todd, Primal–dual interior-point methods for self-scaled cones, SIAM J. Optim. 8 (1998), pp. 324–364 doi: 10.1137/S1052623495290209
- M. Overton, On minimizing the maximum eigenvalue of a symmetric matrix, SIAM. J. Matrix Anal. Appl. 9 (1988), pp. 256–268 doi: 10.1137/0609021
- M. Overton, Large-scale optimization of eigenvalues, SIAM J. Optim. 2 (1992), pp. 88–120 doi: 10.1137/0802007
- J. Peng, C. Roos and T. Terlaky, Self-regular functions and new search directions for linear and semidefinite optimization, Math. Program. 93 (2002), pp. 129–171 doi: 10.1007/s101070200296
- M. J. Todd, K. C. Toh and R. H. Tütüncü, On the Nesterov–Todd direction in semidefinite programming, SIAM J. Optim. 8 (1998), pp. 769–796 doi: 10.1137/S105262349630060X
- G. Wang and Y. Bai, A new primal–dual path-following interior-point algorithm for semidefinite optimization, J. Math. Anal. Appl. 353 (2009), pp. 339–343 doi: 10.1016/j.jmaa.2008.12.016
- G. Wang and Y. Bai, Primal–dual interior-point algorithms for convex quadratic semidefinite optimization, Nonlinear Anal. 71 (2009), pp. 3389–3402 doi: 10.1016/j.na.2009.01.241
- Y. Ye, A class of projective transformations for linear programming, SIAM J. Comput. 19 (1990), pp. 457–466 doi: 10.1137/0219030
- Y. Zhang, On extending some primal–dual interior-point algorithms from linear programming to semidefinite programming, SIAM J. Optim. 8 (1998), pp. 365–386 doi: 10.1137/S1052623495296115
- Y. Zhang and D. Zhang, On polynomial of the Mehrotra-type predictor–corrector interior-point algorithms, Math. Program. 68 (1995), pp. 303–318 doi: 10.1007/BF01585769