Citation: |
[1] |
T. Fu. Liang and H. Wen. Cheng, Multi-objective aggregate production planning decisions using two-phase fuzzy goal programming method, Journal of Industrial and Management Optimization, 7 (2011), 365-383. |
[2] |
J. Ramík, Duality in fuzzy linear programming: some new concepts and results, Fuzzy Optimization and Decision Making, 4 (2005), 25-39. |
[3] |
N. M. Amiri and S. H. Nasseri, Duality in fuzzy number linear programming by use of a certain linear ranking function, Applied Mathematics and Computation, 180 (2006), 206-216.doi: 10.1016/j.amc.2005.11.161. |
[4] |
J. Ramík, Optimal solutions in optimization problem with objective function depending on fuzzy parameters, Fuzzy Sets and Systems, 158 (2007), 1873-1881.doi: 10.1016/j.fss.2007.04.003. |
[5] |
C. Zhang, X. Yuan and E. S. Lee, Duality theory in fuzzy mathematical programming problems with fuzzy coefficients, Computers and Mathematics with Applications, 49 (2005), 1709-1730. |
[6] |
H. C. Wu, Duality theory in fuzzy optimization problems formulated by the Wolfe's primal and dual pair, Fuzzy Optimization and Decision Making, 6 (2007), 179-198.doi: 10.1007/s10700-007-9014-x. |
[7] |
H. C. Wu, Duality theorems in fuzzy mathematical programming problems based on the concept of necessity, Fuzzy Sets and Systems, 139 (2003), 363-377.doi: 10.1016/S0165-0114(02)00575-4. |
[8] |
H. C. Wu, Duality theory in fuzzy optimization problems, Fuzzy Optimization and Decision Making, 3 (2004), 345-365. |
[9] |
Z. T. Gong and H. X. Li, Saddle point optimality conditions in fuzzy optimization problems, Fuzzy Information and Engineering, AISC, 2 (2009), 7-14. |
[10] |
H. C. Wu, The optimality conditions for optimization problems with convex constraints and multiple fuzzy-valued objective functions, Fuzzy Optimization and Decision Making, 8 (2009), 295-321. |
[11] |
D. Dentcheva and W. Römisch , Duality gaps in nonconvex stochastic optimization, Mathematical Programming, Ser. A, 101 (2004), 515-535. |
[12] |
L. A. Korf, Stochastic programming duality: $L^{\propto}$ multipliers for unbounded constraints with an application to mathematical finance, Mathematical Programming, Ser. A, 99 (2004), 241-259. |
[13] |
D. Dentcheva and A.Ruszczyński, Optimality and duality theory for stochastic optimization problems with nonlinear dominance constraints, Mathematical Programming, Ser. A, 99 (2004), 329-350. |
[14] |
A. Shapiro, Stochastic programming approach to optimization under uncertainty, Mathematical Programming, Ser. B, 112 (2008), 183-220. |
[15] |
H. Zhu, Convex duality for finite-fuel problems in singular stochastic control, Journal of Optimization Theory and Applications, 75 (1992), 154-181. |
[16] |
H. C. Wu, Duality theory for optimization problems with interval-valued objective functions, Journal of Optimization Theory and Applications, 144 (2010), 615-628. |
[17] |
H. C. Wu, On interval-valued nonlinear programming problems, Journal of Mathematical Analysis and Application, 338 (2008), 299-316. |
[18] |
H. C. Wu, Wolfe duality for interval-valued optimization, Journal of Optimization Theory and Applications, 138 (2008), 497-509. |
[19] |
H. C. Zhou and Y. J. Wang, Optimality condition and mixed duality for interval-valued optimization. Fuzzy Information and Engineering, AISC, 62 (2009), 1315-1323. |
[20] |
H. C. Wu, The Karush-Kuhn-Tucker optimality conditions in an optimization problem with interval-valued objective function, European Journal of Operational Research, 176 (2007), 46-59. |
[21] |
H. C. Wu, The Karush-Kuhn-Tucker optimality conditions in multiobjective programming problems with interval-valued objective functions, European Journal of Operational Research, 196 (2009), 49-60. |
[22] |
R. E. Moore, "Method and Applications of Interval Analysis," SIAM, Philadelphia, 1979. |
[23] |
A. Prékopa, "Stochastic Programming: Mathematics and Its Applications," Kluwer Academic Publishers Group, Dordrecht, 1995. |
[24] |
M. Schechter, More on subgradient duality, Journal of Mathematical Analysis and Application, 71 (1979), 251-262. |