-
Previous Article
Ant colony optimization for optimum service times in a Bernoulli schedule vacation interruption queue with balking and reneging
- JIMO Home
- This Issue
-
Next Article
Nonsingular $H$-tensor and its criteria
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.
doi: 10.1007/BF02196591. |
[2] |
F. Giannessi, Theorems of the alternative and optimality conditions,, J. Optim. Theory Appl., 42 (1984), 331.
doi: 10.1007/BF00935321. |
[3] |
F. Giannessi, Constrained Optimization and Image Space Analysis,, Springer, (2005).
|
[4] |
F. Giannessi and G. Mastroeni, Separation of sets and Wolfe duality,, J. Global Optim., 42 (2008), 401.
doi: 10.1007/s10898-008-9301-2. |
[5] |
C. Helmberg, Semidefinite programming,, European J. Oper. Res., 137 (2002), 461.
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.
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.
doi: 10.1007/s11425-011-4287-5. |
[8] |
D. T. Luc, Theory of Vector Optimization,, Springer Verlag, (1989).
|
[9] |
Y. Nesterov and A. Nemirovskii, Interior-point Polynomial Algorithms in Convex Programming,, SIAM Studies in Applied Mathematics, (1994).
doi: 10.1137/1.9781611970791. |
[10] |
R. T. Rockafellar, Convex Analysis,, Princeton University Press, (1970).
|
[11] |
A. Shapiro and K. Scheinberg, Duality and optimality conditions,, in Handbook of Semidefinite Programming: Theory, (2000), 67.
doi: 10.1007/978-1-4615-4381-7_4. |
[12] |
L. Vandenberghe and S. Boyd, Semidefinite programming,, SIAM Rev., 38 (1996), 49.
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.
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.
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), (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.
doi: 10.1007/BF02196591. |
[2] |
F. Giannessi, Theorems of the alternative and optimality conditions,, J. Optim. Theory Appl., 42 (1984), 331.
doi: 10.1007/BF00935321. |
[3] |
F. Giannessi, Constrained Optimization and Image Space Analysis,, Springer, (2005).
|
[4] |
F. Giannessi and G. Mastroeni, Separation of sets and Wolfe duality,, J. Global Optim., 42 (2008), 401.
doi: 10.1007/s10898-008-9301-2. |
[5] |
C. Helmberg, Semidefinite programming,, European J. Oper. Res., 137 (2002), 461.
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.
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.
doi: 10.1007/s11425-011-4287-5. |
[8] |
D. T. Luc, Theory of Vector Optimization,, Springer Verlag, (1989).
|
[9] |
Y. Nesterov and A. Nemirovskii, Interior-point Polynomial Algorithms in Convex Programming,, SIAM Studies in Applied Mathematics, (1994).
doi: 10.1137/1.9781611970791. |
[10] |
R. T. Rockafellar, Convex Analysis,, Princeton University Press, (1970).
|
[11] |
A. Shapiro and K. Scheinberg, Duality and optimality conditions,, in Handbook of Semidefinite Programming: Theory, (2000), 67.
doi: 10.1007/978-1-4615-4381-7_4. |
[12] |
L. Vandenberghe and S. Boyd, Semidefinite programming,, SIAM Rev., 38 (1996), 49.
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.
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.
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), (2000).
|
[1] |
Xian-Jun Long, Nan-Jing Huang, Zhi-Bin Liu. Optimality conditions, duality and saddle points for nondifferentiable multiobjective fractional programs. Journal of Industrial & Management Optimization, 2008, 4 (2) : 287-298. doi: 10.3934/jimo.2008.4.287 |
[2] |
Bhawna Kohli. Sufficient optimality conditions using convexifactors for optimistic bilevel programming problem. Journal of Industrial & Management Optimization, 2020 doi: 10.3934/jimo.2020114 |
[3] |
Jiawei Chen, Shengjie Li, Jen-Chih Yao. Vector-valued separation functions and constrained vector optimization problems: optimality and saddle points. Journal of Industrial & Management Optimization, 2020, 16 (2) : 707-724. doi: 10.3934/jimo.2018174 |
[4] |
Honglei Xu, Kok Lay Teo, Weihua Gui. Necessary and sufficient conditions for stability of impulsive switched linear systems. Discrete & Continuous Dynamical Systems - B, 2011, 16 (4) : 1185-1195. doi: 10.3934/dcdsb.2011.16.1185 |
[5] |
M. Soledad Aronna. Second order necessary and sufficient optimality conditions for singular solutions of partially-affine control problems. Discrete & Continuous Dynamical Systems - S, 2018, 11 (6) : 1233-1258. doi: 10.3934/dcdss.2018070 |
[6] |
Ram U. Verma. General parametric sufficient optimality conditions for multiple objective fractional subset programming relating to generalized $(\rho,\eta,A)$ -invexity. Numerical Algebra, Control & Optimization, 2011, 1 (3) : 333-339. doi: 10.3934/naco.2011.1.333 |
[7] |
Hongwei Lou. Second-order necessary/sufficient conditions for optimal control problems in the absence of linear structure. Discrete & Continuous Dynamical Systems - B, 2010, 14 (4) : 1445-1464. doi: 10.3934/dcdsb.2010.14.1445 |
[8] |
Stepan Sorokin, Maxim Staritsyn. Feedback necessary optimality conditions for a class of terminally constrained state-linear variational problems inspired by impulsive control. Numerical Algebra, Control & Optimization, 2017, 7 (2) : 201-210. doi: 10.3934/naco.2017014 |
[9] |
Piernicola Bettiol, Nathalie Khalil. Necessary optimality conditions for average cost minimization problems. Discrete & Continuous Dynamical Systems - B, 2019, 24 (5) : 2093-2124. doi: 10.3934/dcdsb.2019086 |
[10] |
Shahlar F. Maharramov. Necessary optimality conditions for switching control problems. Journal of Industrial & Management Optimization, 2010, 6 (1) : 47-55. doi: 10.3934/jimo.2010.6.47 |
[11] |
Cristian Dobre. Mathematical properties of the regular *-representation of matrix $*$-algebras with applications to semidefinite programming. Numerical Algebra, Control & Optimization, 2013, 3 (2) : 367-378. doi: 10.3934/naco.2013.3.367 |
[12] |
Vladimir Gaitsgory, Alex Parkinson, Ilya Shvartsman. Linear programming based optimality conditions and approximate solution of a deterministic infinite horizon discounted optimal control problem in discrete time. Discrete & Continuous Dynamical Systems - B, 2019, 24 (4) : 1743-1767. doi: 10.3934/dcdsb.2018235 |
[13] |
Yi Xu, Wenyu Sun. A filter successive linear programming method for nonlinear semidefinite programming problems. Numerical Algebra, Control & Optimization, 2012, 2 (1) : 193-206. doi: 10.3934/naco.2012.2.193 |
[14] |
Bernard Dacorogna. Necessary and sufficient conditions for strong ellipticity of isotropic functions in any dimension. Discrete & Continuous Dynamical Systems - B, 2001, 1 (2) : 257-263. doi: 10.3934/dcdsb.2001.1.257 |
[15] |
Zuohuan Zheng, Jing Xia, Zhiming Zheng. Necessary and sufficient conditions for semi-uniform ergodic theorems and their applications. Discrete & Continuous Dynamical Systems - A, 2006, 14 (3) : 409-417. doi: 10.3934/dcds.2006.14.409 |
[16] |
Ana Cristina Barroso, José Matias. Necessary and sufficient conditions for existence of solutions of a variational problem involving the curl. Discrete & Continuous Dynamical Systems - A, 2005, 12 (1) : 97-114. doi: 10.3934/dcds.2005.12.97 |
[17] |
Mansoureh Alavi Hejazi, Soghra Nobakhtian. Optimality conditions for multiobjective fractional programming, via convexificators. Journal of Industrial & Management Optimization, 2020, 16 (2) : 623-631. doi: 10.3934/jimo.2018170 |
[18] |
Manil T. Mohan. First order necessary conditions of optimality for the two dimensional tidal dynamics system. Mathematical Control & Related Fields, 2020 doi: 10.3934/mcrf.2020045 |
[19] |
Nuno R. O. Bastos, Rui A. C. Ferreira, Delfim F. M. Torres. Necessary optimality conditions for fractional difference problems of the calculus of variations. Discrete & Continuous Dynamical Systems - A, 2011, 29 (2) : 417-437. doi: 10.3934/dcds.2011.29.417 |
[20] |
Sofia O. Lopes, Fernando A. C. C. Fontes, Maria do Rosário de Pinho. On constraint qualifications for nondegenerate necessary conditions of optimality applied to optimal control problems. Discrete & Continuous Dynamical Systems - A, 2011, 29 (2) : 559-575. doi: 10.3934/dcds.2011.29.559 |
2019 Impact Factor: 1.366
Tools
Metrics
Other articles
by authors
[Back to Top]