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Duality formulations in semidefinite programming
1. | Department of Mathematics and Computer Science, Northern Michigan University, Marquette, MI 49855, United States |
2. | Department of Mathematics, Nantong Vacational College, Nantong 226007, China, China |
References:
[1] |
G. Barker and D. Carlson, Cones of diagonally dominant matrices, Pacific J. Math., 57 (1975), 15-32. |
[2] |
J. Bonnans and A. Shapiro, "Perturbation Analysis of Optimization Problems," Springer, New York, 2000. |
[3] |
J. Borwein and H. Wolkowicz, Facial reduction for a cone-convex programming problem,, J. Austral. Math. Soc. Ser. A, 30 (): 369.
|
[4] |
J. Borwein and H. Wolkowicz, Regularizing the abstract convex program, J. Math. Anal. Appl., 83 (1981), 495-530.
doi: 10.1016/0022-247X(81)90138-4. |
[5] |
E. de Klerk, C. Roos and T. Terlaky, Infeasible start semidefinite programming algorithms via self-dual embeddings, Fields Inst. Commun., 18 (1998), 215-236. |
[6] |
K. Kortanek and Q. Zhang, Perfect duality in semi-infinite and semidefinite programming, Math. Program., Ser. A, 91 (2001), 127-144. |
[7] |
Z. Luo, J. Sturm and S. Zhang, "Duality Results for Conic Convex Programming," Technical Report, Econometric Institute Report No. 9719/A, Econometric Institute, Erasumus University, Rotterdam, The Netherlands, April 1997. |
[8] |
M. Ramana, An exact duality theory for semidefinite programming and its complexity implications, Math. Program., Ser. B, 77 (1997), 129-162. |
[9] |
M. Ramana, L. Tunçel and H. Wolkowicz, Strong duality for semidefinite programming, SIAM J. Optim., 7 (1997), 641-662. |
[10] |
R. Rockafellar, "Convex Analysis," Princeton University Press, Princeton, New Jersey, 1970. |
[11] |
J. Sturm, "Primal-Dual Interior Point Approach to Semidefinite Programming," Ph.D thesis, Erasmus University, 1997. |
[12] |
M. Todd, Semidefinite optimization, Acta. Numer., 10 (2001), 515-560.
doi: 10.1017/S0962492901000071. |
[13] |
L. Vandenberghe and S. Boyd, Semidefinite programming, SIAM Review, 38 (1996), 49-95.
doi: 10.1137/1038003. |
[14] |
H. Wolkowicz, Some applications of optimization in matrix theory, Linear Algebra Appl., 40 (1981), 101-118.
doi: 10.1016/0024-3795(81)90143-9. |
[15] |
Q. Zhang, Embedding methods for semidefinite programming,, submitted for publication., ().
|
show all references
References:
[1] |
G. Barker and D. Carlson, Cones of diagonally dominant matrices, Pacific J. Math., 57 (1975), 15-32. |
[2] |
J. Bonnans and A. Shapiro, "Perturbation Analysis of Optimization Problems," Springer, New York, 2000. |
[3] |
J. Borwein and H. Wolkowicz, Facial reduction for a cone-convex programming problem,, J. Austral. Math. Soc. Ser. A, 30 (): 369.
|
[4] |
J. Borwein and H. Wolkowicz, Regularizing the abstract convex program, J. Math. Anal. Appl., 83 (1981), 495-530.
doi: 10.1016/0022-247X(81)90138-4. |
[5] |
E. de Klerk, C. Roos and T. Terlaky, Infeasible start semidefinite programming algorithms via self-dual embeddings, Fields Inst. Commun., 18 (1998), 215-236. |
[6] |
K. Kortanek and Q. Zhang, Perfect duality in semi-infinite and semidefinite programming, Math. Program., Ser. A, 91 (2001), 127-144. |
[7] |
Z. Luo, J. Sturm and S. Zhang, "Duality Results for Conic Convex Programming," Technical Report, Econometric Institute Report No. 9719/A, Econometric Institute, Erasumus University, Rotterdam, The Netherlands, April 1997. |
[8] |
M. Ramana, An exact duality theory for semidefinite programming and its complexity implications, Math. Program., Ser. B, 77 (1997), 129-162. |
[9] |
M. Ramana, L. Tunçel and H. Wolkowicz, Strong duality for semidefinite programming, SIAM J. Optim., 7 (1997), 641-662. |
[10] |
R. Rockafellar, "Convex Analysis," Princeton University Press, Princeton, New Jersey, 1970. |
[11] |
J. Sturm, "Primal-Dual Interior Point Approach to Semidefinite Programming," Ph.D thesis, Erasmus University, 1997. |
[12] |
M. Todd, Semidefinite optimization, Acta. Numer., 10 (2001), 515-560.
doi: 10.1017/S0962492901000071. |
[13] |
L. Vandenberghe and S. Boyd, Semidefinite programming, SIAM Review, 38 (1996), 49-95.
doi: 10.1137/1038003. |
[14] |
H. Wolkowicz, Some applications of optimization in matrix theory, Linear Algebra Appl., 40 (1981), 101-118.
doi: 10.1016/0024-3795(81)90143-9. |
[15] |
Q. Zhang, Embedding methods for semidefinite programming,, submitted for publication., ().
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