Journal of Applied Analysis 11 (2005), No. 2, 225--245
Copyright Heldermann Verlag 2005
Optimality Conditions and Duality for Multiobjective Control Problems
T. R. Gulati
Dept. of Mathematics, Indian Institute of Technology, Roorkee - 247 667, India
trgorfma@iitr.ernet.in
I. Husain
Dept. of Mathematics, National Institute of Technology, Hazratbal, Srinagar - 190 006, India
ihusain11@yahoo.com
A. Ahmed
Dept. of Statistics, University of Kashmir, Hazratbal, Srinagar - 190 006, Kashmir, India
aqlstat@yahoo.co.in
Fritz John and Kuhn-Tucker type necessary optimality conditions for a Pareto optimal (efficient) solution of a multiobjective control problem are obtained by first reducing the multiobjective control problem to a system of single objective control problems, and then using already established optimality conditions. As an application of Kuhn-Tucker type optimality conditions, Wolfe and Mond-Weir type dual multiobjective control problems are formulated and usual duality results are established under invexity/generalized invexity, relating properly efficient solutions of the primal and dual problems. Wolfe and Mond-Weir type dual multiobjective control problems with free boundary conditions are also presented.
Keywords: Pareto optimality, efficiency, proper efficiency, multiobjective control problems, duality, free boundary conditions, static problems.
MSC: 90C46, 90C29
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