Optimality conditions and duality for multiobjective control problems

• Autorzy: Gulati T. R. , Husain I. , Ahmed A.
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Pareto optimality; efficiency; proper efficiency; multiobjective control problems; duality; free boundary conditions; static problems

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2005
• Tom: Vol. 11, nr 2
• Strony: 225--245
• Opis fizyczny: Bibliogr. 8 poz.

Twórcy

autor

Gulati T. R.

• Department of Mathematics, Indian Institute of Technology, Roorkee-247 667, India

autor

Husain I.

• Department of Mathematics, National Institute of Technology, Hazratbal, Srinagar-190 006, Kashmir, India

autor

Ahmed A.

• Department of Statistics, University of Kashmir, Hazratbal, Srinagar -190 006, Kashmir, India

Bibliografia

• [1] Chandra, S., Craven, B. D., Husain, I., A class of nondifferentiable control problems, J. Optim. Theory Appl. 56 (1988), 227-243.
• [2] Craven, B. D., Mathematical Programming and Control Theory, Chapman and Hall, London, 1978.
• [3] Geoffrion, A. M., Proper efficiency and the theory of vector maximization, J. Math. Anal. Appl. 22 (1968), 618-630.
• [4] Gulati, T. R., Islam, M. A., Efficiency and proper efficiency in differentiable multi-objective programming, Ganit 9 (1989), 55-62.
• [5] 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.
• [6] Kanniappan, P., Necessary conditions for optimality of nondifferentiable convex multiobjective programming, J. Optim. Theory Appl. 40 (1983), 167-174.
• [7] Mond, B., Hanson, M. A., Duality for control problems, SIAM J. Control 6 (1968), 114-120.
• [8] Mond, B., Smart, I., Duality and. sufficiency in control problems with invexity, J. Math. Anal. Appl. 136 (1988), 325-333.