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Semidefinite programming via image space analysis
| 1. | College of Economics and Business Administration, Chongqing University, Chongqing 400044, China |
References:
| [1] |
P. H. Dien, G. Mastroeni, M. Pappalardo and P. H. Quang, Regularity conditions for constrained extremum problems via image space, J. Optim. Theory Appl., 80 (1994), 19-37.
doi: 10.1007/BF02196591. |
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F. Giannessi, Theorems of the alternative and optimality conditions, J. Optim. Theory Appl., 42 (1984), 331-365.
doi: 10.1007/BF00935321. |
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F. Giannessi, Constrained Optimization and Image Space Analysis, Springer, New York, 2005. |
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F. Giannessi and G. Mastroeni, Separation of sets and Wolfe duality, J. Global Optim., 42 (2008), 401-412.
doi: 10.1007/s10898-008-9301-2. |
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C. Helmberg, Semidefinite programming, European J. Oper. Res., 137 (2002), 461-482.
doi: 10.1016/S0377-2217(01)00143-6. |
| [6] |
J. Li and N. J. Huang, Image space analysis for vector variational inequalities with matrix inequality constraints and applications, J. Optim. Theory Appl., 145 (2010), 459-477.
doi: 10.1007/s10957-010-9691-4. |
| [7] |
J. Li and N. J. Huang, Image space analysis for variational inequalities with cone constraints and applications to traffic equilibria, Sci. China Math., 55 (2012), 851-868.
doi: 10.1007/s11425-011-4287-5. |
| [8] |
D. T. Luc, Theory of Vector Optimization, Springer Verlag, Berlin, 1989. |
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Y. Nesterov and A. Nemirovskii, Interior-point Polynomial Algorithms in Convex Programming, SIAM Studies in Applied Mathematics, Philadelphia, 1994.
doi: 10.1137/1.9781611970791. |
| [10] |
R. T. Rockafellar, Convex Analysis, Princeton University Press, Princeton, 1970. |
| [11] |
A. Shapiro and K. Scheinberg, Duality and optimality conditions, in Handbook of Semidefinite Programming: Theory, Algorithms and Applications (eds. H. Wolkowicz, R. Saigal and L. Vandenberghe), Kluwer Acad. Publ., 27, Boston, MA, 2000, 67-110.
doi: 10.1007/978-1-4615-4381-7_4. |
| [12] |
L. Vandenberghe and S. Boyd, Semidefinite programming, SIAM Rev., 38 (1996), 49-95.
doi: 10.1137/1038003. |
| [13] |
G. Wanka, R. I. Boţ and S. M. Grad, Multiobjective duality for convex semidefinite programming problems, Z. Anal. Anwendungen, 22 (2003), 711-728.
doi: 10.4171/ZAA/1169. |
| [14] |
S. K. Zhu and S. J. Li, Unified duality theory for constrained extremum problems. Part I: Image space analysis, J. Optim. Theory Appl., 161 (2014), 738-762.
doi: 10.1007/s10957-013-0468-4. |
| [15] |
J. Zowe and M. Kočvara, Semidefinite programming, in Modern Optimization and its Applications in Engineering (eds. A. Ben-Tal and A. Nemirovski), Haifa (Israel), Technion, 2000. |
show all references
References:
| [1] |
P. H. Dien, G. Mastroeni, M. Pappalardo and P. H. Quang, Regularity conditions for constrained extremum problems via image space, J. Optim. Theory Appl., 80 (1994), 19-37.
doi: 10.1007/BF02196591. |
| [2] |
F. Giannessi, Theorems of the alternative and optimality conditions, J. Optim. Theory Appl., 42 (1984), 331-365.
doi: 10.1007/BF00935321. |
| [3] |
F. Giannessi, Constrained Optimization and Image Space Analysis, Springer, New York, 2005. |
| [4] |
F. Giannessi and G. Mastroeni, Separation of sets and Wolfe duality, J. Global Optim., 42 (2008), 401-412.
doi: 10.1007/s10898-008-9301-2. |
| [5] |
C. Helmberg, Semidefinite programming, European J. Oper. Res., 137 (2002), 461-482.
doi: 10.1016/S0377-2217(01)00143-6. |
| [6] |
J. Li and N. J. Huang, Image space analysis for vector variational inequalities with matrix inequality constraints and applications, J. Optim. Theory Appl., 145 (2010), 459-477.
doi: 10.1007/s10957-010-9691-4. |
| [7] |
J. Li and N. J. Huang, Image space analysis for variational inequalities with cone constraints and applications to traffic equilibria, Sci. China Math., 55 (2012), 851-868.
doi: 10.1007/s11425-011-4287-5. |
| [8] |
D. T. Luc, Theory of Vector Optimization, Springer Verlag, Berlin, 1989. |
| [9] |
Y. Nesterov and A. Nemirovskii, Interior-point Polynomial Algorithms in Convex Programming, SIAM Studies in Applied Mathematics, Philadelphia, 1994.
doi: 10.1137/1.9781611970791. |
| [10] |
R. T. Rockafellar, Convex Analysis, Princeton University Press, Princeton, 1970. |
| [11] |
A. Shapiro and K. Scheinberg, Duality and optimality conditions, in Handbook of Semidefinite Programming: Theory, Algorithms and Applications (eds. H. Wolkowicz, R. Saigal and L. Vandenberghe), Kluwer Acad. Publ., 27, Boston, MA, 2000, 67-110.
doi: 10.1007/978-1-4615-4381-7_4. |
| [12] |
L. Vandenberghe and S. Boyd, Semidefinite programming, SIAM Rev., 38 (1996), 49-95.
doi: 10.1137/1038003. |
| [13] |
G. Wanka, R. I. Boţ and S. M. Grad, Multiobjective duality for convex semidefinite programming problems, Z. Anal. Anwendungen, 22 (2003), 711-728.
doi: 10.4171/ZAA/1169. |
| [14] |
S. K. Zhu and S. J. Li, Unified duality theory for constrained extremum problems. Part I: Image space analysis, J. Optim. Theory Appl., 161 (2014), 738-762.
doi: 10.1007/s10957-013-0468-4. |
| [15] |
J. Zowe and M. Kočvara, Semidefinite programming, in Modern Optimization and its Applications in Engineering (eds. A. Ben-Tal and A. Nemirovski), Haifa (Israel), Technion, 2000. |
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