Journal of Applied Analysis 14 (2008), No. 1, 027--042
Copyright Heldermann Verlag 2008
Sufficiency and Duality in Control Problems with Generalized Invexity
Iqbal Husain
Dept. of Mathematics, Jaypee Institute of Engineering and Technology, AB-Road Raghogarh, Guna (M.P.) 473 226, India
iqbal.husain@jiet.ac.in
Aquil Ahmed
Department of Statistics, University of Kashmir, Hazratbal, Srinagar 190 006, India
aqlstat@yahoo.com
Bilal Ahmad
Department of Statistics, University of Kashmir, Hazratbal, Srinagar 190 006, India
bilal.jalali@yahoo.com
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 problems. It is pointed out that these results can be applied to the control problem with free boundary conditions and have linkage with results for nonlinear programming problems in the presence of inequality and equality constraints already established in the literature.
Keywords: Sufficient optimality criteria, control problem, Mond-Weir type dual, control problem with free boundary, on-linear programming problem.
MSC: 90C30, 90C11, 90C20, 90C26
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