An Interior-Point Perspective on Sensitivity Analysis in Semidefinite Programming

References

• Adler I., Monteiro R. D. C. A geometric view of parametric linear programming. Algorithmica (1992) 8:161–176Crossref, Google Scholar
• Alizadeh F., Haeberly J-P. A., Overton M. L. Complementarity and nondegeneracy in semidefinite programming. Math. Programming (1997) 77:111–128Crossref, Google Scholar
• Alizadeh F., Haeberly J-P. A., Overton M. L. Primal-dual interior-point methods for semidefinite programming: Convergence rates, stability, and numerical results. SIAM J. Optim. (1998) 8:746–768Crossref, Google Scholar
• Barker G. P., Carlson D. Cones of diagonally dominant matrices. Pacific J. Math. (1975) 57:15–32Crossref, Google Scholar
• Bonnans J. F., Shapiro A.Perturbation Analysis of Optimization Problems (2000) (Springer, New York) Crossref, Google Scholar
• Goldfarb D., Scheinberg K. Interior point trajectories in semidefinite programs. SIAM J. Optim. (1998) 8:871–886Crossref, Google Scholar
• Goldfarb D., Scheinberg K. On parametric semidefinite programming. Appl. Numer. Math.: Trans. IMACS (1999) 29(3):361–377Crossref, Google Scholar
• Golub G. H., Van Loan C. F.Matrix Computations (1996) 3rd ed.(The Johns Hopkins University Press, Baltimore, MD) Google Scholar
• Halicka M., de Klerk E., Roos C. Limiting behavior of the central path in semidefinite optimization. (2002a) . Technical report, Faculty ITS, Delft University of Technology, Delft, The NetherlandsGoogle Scholar
• Halicka M., de Klerk E., Roos C. On the convergence of the central path in semidefinite optimization. SIAM J. Optim. (2002b) 12(4):1090–1099Crossref, Google Scholar
• Helmberg C., Rendl F., Vanderbei R. J., Wolkowicz H. An interior-point method for semidefinite programming. SIAM J. Optim. (1996) 6:342–361Crossref, Google Scholar
• Jansen B., de Jong J. J., Roos C., Terlaky T. Sensitivity analysis in linear programming: Just be careful!. Eur. J. Oper. Res. (1997) 101:15–28Crossref, Google Scholar
• Kim W-J., Park C-K., Park S. An ε-sensitivity analysis in the primal-dual interior point method. Eur. J. Oper. Res. (1999) 116(3):629–639Crossref, Google Scholar
• Kojima M., Shindoh S., Hara S. Interior point methods for the monotone semidefinite linear complementarity problem in symmetric matrices. SIAM J. Optim. (1997) 7:86–125Crossref, Google Scholar
• Luo Z-Q., Sturm J. F., Zhang S. Superlinear convergence of a symmetric primal-dual path-following algorithm for semidefinite programming. SIAM J. Optim. (1998) 8:59–81Crossref, Google Scholar
• Monteiro R. D. C. Primal-dual path-following algorithms for semidefinite programming. SIAM J. Optim. (1997) 7:663–678Crossref, Google Scholar
• Monteiro R. D. C. Polynomial convergence of primal-dual algorithms for semidefinite programming based on the Monteiro and Zhang family of directions. SIAM J. Optim. (1998) 8:797–812Crossref, Google Scholar
• Monteiro R. D. C., Zanjácomo P. R. A note on the existence of the Alizadeh-Haeberly-Overton direction for semidefinite programming. Math. Programming (1997) 78:393–396Crossref, Google Scholar
• Monteiro R. D. C., Zhang Y. A unified analysis for a class of path-following primal-dual interior-point algorithms for semidefinite programming. Math. Programming (1998) 81:281–299Crossref, Google Scholar
• Nayakkankuppam M. V., Overton M. L. Conditioning of semidefinite programs. Math. Programming (1999) 85(3):525–540Crossref, Google Scholar
• Nesterov Y., Nemirovskii A. S.Interior Point Polynomial Algorithms in Convex Programming (1994) (SIAM Publications, Philadelphia, PA) Crossref, Google Scholar
• Nesterov Yu. E., Todd M. J. Self-scaled barriers and interior-point methods for convex programming. Math. Oper. Res. (1997) 22:1–42Link, Google Scholar
• Nesterov Yu. E., Todd M. J. Primal-dual interior-point methods for self-scaled cones. SIAM J. Optim. (1998) 8:324–362Crossref, Google Scholar
• Nunez M. A., Freund R. M. Condition-measure bounds on the behavior of the central trajectory of a semidefinite program. SIAM J. Optim. (2001) 11(3):818–836Crossref, Google Scholar
• Pataki G., Wolkowicz H., Saigal R., Vandenberghe L. Geometry of semidefinite programming. Handbook of Semidefinite Programming: Theory, Algorithms, and Applications (2000) (Kluwer Academic Publishers, Boston, MA) Crossref, Google Scholar
• Shida M., Shindoh S., Kojima M. Existence of search directions in interior-point algorithms for the SDP and the monotone SDLCP. SIAM J. Optim. (1998) 8:387–396Crossref, Google Scholar
• Stewart G. W. Error and perturbation bounds for subspaces associated with certain eigenvalue problems. SIAM Rev. (1973) 15(4):727–764Crossref, Google Scholar
• Sturm J. F., Zhang S. On sensitivity of central solutions in semidefinite programming. Math. Programming (2001) 90(2):205–227Crossref, Google Scholar
• Todd M. J. A study of search directions in primal-dual interior-point methods for semidefinite programming. Optim. Methods Software (1999) 11–12:1–46Google Scholar
• Todd M. J., Toh K. C., Tütüncü R. H. On the Nesterov-Todd direction in semidefinite programming. SIAM J. Optim. (1998) 8(3):769–796Crossref, Google Scholar
• Yıldırım E. A. Unifying optimal partition approach to sensitivity analysis in conic optimization. J. Optim. Theory Appl. (2003) . ForthcomingGoogle Scholar
• Yıldırım E. A., Todd M. J. Sensitivity analysis in linear programming and semidefinite programming using interior-point methods. Math. Programming (2001) 90(2):229–261Crossref, Google Scholar
• Yıldırım E. A., Todd M. J. An interior-point approach to sensitivity analysis in degenerate linear programs. SIAM J. Optim. (2002) 12(3):692–714Crossref, Google Scholar
• Yıldırım E. A., Wright S. J. Warm-start strategies in interior-point methods for linear programming. SIAM J. Optim. (2002) 12(3):782–810Crossref, Google Scholar
• Zhang Y. On extending some primal-dual interior-point algorithms from linear programming to semidefinite programming. SIAM J. Optim. (1998) 8:365–386Crossref, Google Scholar