Sufficiency and duality in multiobjective programming with generalized (F, ρ)-convexity

• Autorzy: Ahmad I.
• Języki publikacji: EN

Abstrakty

EN

A multiobjective nonlinear programming problem is considered. Sufficiency theorems are derived for efficient and properly efficient solutions under generalized (F, ρ)-convexity assumptions. Weak, strong and strict converse duality theorems are established for a general Mond-Weir type dual relating properly efficient solutions of the primal and aual problems.

Słowa kluczowe

PL

90C29; 90C30; 90C46

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2005
• Tom: Vol. 11, nr 1
• Strony: 19--33
• Opis fizyczny: Bibliogr. 9 poz.

Twórcy

autor

Ahmad I.

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

Bibliografia

• [1] Bector, C. R., Klassen, J. E., Duality for a nonlinear programming problem, Utilitas Math. 11 (1977), 87-99.
• [2] Geoffrion, A. M., Proper efficiency and the theory of vector maximization, J. Math. Anal. Appl. 22 (1968), 618-630.
• [3] Gulati, T. R., Islam, M. A., Sufficiency and duality in multiobjective programming involving generalized, F-convex functions, J. Math. Anal. Appl. 183 (1994), 181-195.
• [4] Hanson, M. A., Mond, B., Further generalizations of convexity in mathematical programming, J. Inform. Optim. Sci. 3 (1982), 25-32.
• [5] Mahajan, D. G., Vartak, M. N., Generalization of some duality theorems in nonlinear programming, Math. Program. 12 (1977), 293-317.
• [6] Mond, B., Weir, T., Generalized concavity and, duality, in „Generalized Concavity in Optimization and Economics”, S. Schaible and W. T. Ziemba, eds., Academic Press, New York, 1981, 263-279.
• [7] Preda, V., On efficiency and duality for multiobjective programs, J. Math. Anal. Appl. 166 (1992), 265-277.
• [8] Vial, J. P., Strong and weak convexity of sets and functions, Math. Oper. Res. 8 (1983), 231-259.
• [9] Weir, T., Proper efficiency and duality for vector valued, optimization problems, J. Austral. Math. Soc. Ser. A 43 (1987), 21-34.