Sufficiency and duality in control problems with generalized invexity

• Autorzy: Husain I , Ahmed A. , Ahmed B.
• Języki publikacji: EN

Abstrakty

EN

Sufficient optimality criteria are derived for a control problem under generalized invexity. A Mond-Weir type dual to the control problem is proposed and various duality theorems are validated under generalized invexity assumptions on functionals appearing in the the problems. It is pointed out that these results can be applied to the control problem with free boundery conditions and have linkage with results for nonlinear programming problems in the presence of inequality and equality constraints already established in the literature.

Słowa kluczowe

EN

90C30; 90C11; 90C20; 90C26

PL

90C30; 90C11; 90C20; 90C26

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2008
• Tom: Vol. 14, nr 1
• Strony: 27--42
• Opis fizyczny: Bibliogr. 9 poz.

Twórcy

autor

Husain I

autor

Ahmed A.

autor

Ahmed B.

• Jaypee Institute of Engineering and Technology. Department of Mathematics, AB-Road, Raghogarh, Guna (M.P.) - 473 226, India,

Bibliografia

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• [2] Berkovitz, L. D., Variational methods in problems of control and programming, J. Math. Anal. Appl. 3 (1961), 145-169.
• [3] Craven, B. D., Mathematical Programming and Control Theory, Chapman & Hall, London, 1978.
• [4] Craven, B. D., Glover, B. M., Invex functions and duality, J. Austral. Math. Soc. Ser. A 39 (1985), 1-20.
• [5] Mond, B., Hanson, M. A., Duality for control problems, SIAM J. Control 6 (1968), 114-120.
• [6] Mond, B., Smart, I., Duality and sufficiency in control problems with invexity, J. Math. Anal. Appl. 136(15) (1988), 325-333.
• [7] 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, 263-271.
• [8] Valentine, F. A., The problem of Lagrange with differentiable inequalities as added side constraints, in "Contribution to the Calculus of Variation", 1933-1937, Univ. Chicago Press, Chicago, Illinois, 407-448, 1937.
• [9] Wolfe, P., A duality theorem for nonlinear programming, Quart. Appl. Math. 19 (1961), 239-244.