Second order duality in multiobjective programming

• Autorzy: Ahmad I. , Husain Z.
• Języki publikacji: EN

Abstrakty

EN

A nonlinear multiobjective programming problem is considered. Weak, strong and strict converse duality theorems are established under generalized second order (F, α, ρ, d)-convexity for second order Mangasarian type and general Mond-Weir type vector duals.

Słowa kluczowe

EN

multiobjective programming; second order duality; efficient solution; generalized (F, α, ρ, d)-convexity

PL

programowanie objektywne; rozwiązania efektywne

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2008
• Tom: Vol. 14, nr 1
• Strony: 131--148
• Opis fizyczny: Bibliogr. 19 poz.

Twórcy

autor

Ahmad I.

autor

Husain Z.

• Aligarh Muslim University. Department of Mathematics, Aligarh-202 002, India,

Bibliografia

• [1] Aghezzaf, B., Hachimi, M., Sufficiency and duality in multiobjective progmmming involving generalized (F,p)-convexity, J. Math. Anal. Appl. 258 (2001),617-628.
• [2] Ahmad, I., Sufficiency and duality in multiobjective programming with generalized (F,p)-convexity, J. Appl. Anal. 11 (2005), 19-33.
• [3] Ahmad, I., Husain, Z., Second order (F, a, p, d)-convexity and duality in multiobjective programming, Inform. Sci. 176 (2006), 3094-3103.
• [4] Ahmad, I., Husain, Z., Optimality conditions and duality in nondifferentiable minimax fractional programming with generalized convexity, J. Optim. Theory Appl. 129 (2006), 255-275.
• [5] Ahmad, I., Husain, Z., Duality in nondifferentiable minimax fractional progmmming with generalized convexity, Appl. Math. Comput. 176 (2006), 545-551.
• [6] Chinchuluun, A., Pardalos, P. M., Multiobjective programming problems under generalized convexity, in: "Models and Algorithms for Global Optimization" , Springer Optim. Appl. 4, Springer, New York, 2007,3220.
• [7] Gulati, T. R., Ahmad, I., Agarwal, D., Sufficiency and duality in multi objective programming under generalized type I functions, J. Optim. Theory Appl. 135 (2007), 411-427.
• [8] Gulati, T. R., Islam, M. A., Sufficiency and duality in multiobjective programming involving generalized F-convexfunctions, J. Math. Anal. Appl.183 (1994),181-195.
• [9] Hanson, M. A., Mond, B., Further generalizations of convexity in mathematical programming, J. Inform. Optim. Sci. 3 (1982), 25-32.
• [10] Liang, Z. A., Huang, H. X., Pardalos, P. M., Optimality conditions and duality for a class of nonlinear fractional programming problems, J. Optim. Theory Appl. 110 (2001), 611-619.
• [11] Liang, Z. A., Huang, H. X., Pardalos, P. M., Efficiency conditions and duality for a class of multiobjective fractional programming problems, J. Global Optim. 27 (2003), 447-471.
• [12] Maeda, T ., Constraint qualifications in multiobjective optimization problems: Differentiable case, J. Optim. Theory Appl. 80 (1994), 483-500.
• [13] Mangasarian, O.L., Second and higher order duality in nonlinear programming, J. Math. Anal. Appl. 51 (1975), 607-620.
• [14] Mond, B., Second order duality for nonlinear progmms, Opsearch 11 (1974), 90-99.
• [15] Mond, B., Zhang, J., Duality for multiobjective progmmming involving second order V-invex functions, in: "Proceedings of the Optimization Miniconference", B. M. Glower and V. Jeyakumar (eds.), University of Ballarat, Ballarat (Australia), 1995, 89-100.
• [16] Preda, V., "On efficiency and duality for multiobjective programs, J. Math. Anal. Appl. 166 (1992), 365-377.
• [17] Vial, J. P., Strong and weak convexity of sets and functions, Math. Oper. Res. 8 (1983),231-259.
• [18] Yuan, D. H., Chinchuluun, A., Liu, X. L., Pardalos, P. M., Optimality conditions and duality for multiobjective programming involving (C, α, ρ, d)-type I functions, in: "Generalized Convexity and Generalized Monotonicity" , Lecture Notes in Econom. and Math. Systems 583, Springer, Berlin, 2007, 73-87.
• [19] Zhang, J., Mond, B., Second order duality for multiobjective nonlinear programming involving generalized convexity, in: "Proceedings of the Optimization Miniconference III", B. M. Glower, B.D. Craven and D. Ralph (eds.), University of Ballarat, Ballarat (Australia), 1997, 79-95.