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http://yadda.icm.edu.pl:80/baztech/element/bwmeta1.element.baztech-article-LOD6-0004-0003

Czasopismo

Journal of Applied Analysis

Tytuł artykułu

Sufficiency and duality in control problems with generalized invexity

Autorzy Husain, I  Ahmed, A.  Ahmed, B. 
Treść / Zawartość
Warianty tytułu
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
PL 90C30   90C11   90C20   90C26  
EN 90C30   90C11   90C20   90C26  
Wydawca Walter de Gruyter GmbH & Co. KG
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, iqbal.husain@jiet.ac.in
Bibliografia
[1] Abraham, J., Buie, R. N., Duality in continuous programming and optimal control, Utilitas Math. 17 (1980), 103-119.
[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.
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