MIXED TYPE MULTIOBJECTIVE VARIATIONAL PROBLEMS WITH HIGHER ORDER DERIVATIVES

  • Husain, I. (Department of Mathematics, Jaypee Institute of Engineering and Technology) ;
  • Ahmed, A. (Department of Statistics, University of Kashmir) ;
  • Rumana, G. Mattoo (Department of Statistics, University of Kashmir)
  • Published : 2009.01.31

Abstract

A mixed type dual for multiobjective variational problem involving higher order derivatives is formulated and various duality results under generalized invexity are established. Special cases are generated and it is also pointed out that our results can be viewed as a dynamic generalization of existing results in the static programming.

Keywords

References

  1. C. R. Bector, S.Chandra and I. Husain, Generalized concavity and duality in continuous programming, Utilitas, Mathematica 25 (1984), 171-190.
  2. C. R. Bector and I. Husain, Duality for multiobjective variational problems, Journal of Math. Anal and Appl. 166 (1992), no.1, 214-224. https://doi.org/10.1016/0022-247X(92)90337-D
  3. S. Chandra, B. D. Craven and I. Husain, A class of nondifferentiable continuous programming problem, J. Math. Anal. Appl. 107 (1985) 122-131. https://doi.org/10.1016/0022-247X(85)90357-9
  4. V. Chankong and Y. Y. Haimes, Multiobjective Decision Making: Theory and Methodology, North-Holland, New York, (1983).
  5. M. A. Hanson, Bonds for functionally convex optimal control problems:, J. Math. Anal. Appl. 126 (1987) 469-477. https://doi.org/10.1016/0022-247X(87)90054-0
  6. I. Husain and Z. Jabeen, On variational problems involving higher order derivatives, J.Math. and Computing Vol. 27 (2005), No. 1-2,433-455.
  7. I. Husain, A. Ahmed and Rumana, G.Mattoo, Optimality criteria and duality in multiobjective variational problems involving higher order derivatives, Submitted for publication.
  8. I. Husain and Rumana, G. Mattoo, Multiobjective duality in variational problems with higher order derivatives, Submitted for publication.
  9. B. Mond and I. Smart, Duality with invexity for a class of nondifferentiable static and continuous programming problems, J.Math. Anal. Appl. 136 (1988) 325-333. https://doi.org/10.1016/0022-247X(88)90135-7
  10. B. Mond and M. A. Hanson, Duality for variational problems, J.Math. Anal. Appl.18 (1967) 355-364 https://doi.org/10.1016/0022-247X(67)90063-7
  11. B. Mond, S. Chandra and I. Husain, Duality of variational problems with invexity, J.Math.Anal. Appl. 134 (1988) 322-328. https://doi.org/10.1016/0022-247X(88)90026-1
  12. F. A. Valentine, The problem of Lagrange with differential inequalities as added side conditions, Contributions to calculus of variations, 1933-37, Univ. of Chicago Press, 1937, 407-448.
  13. Z. Xu, Mixed type duality in multiobjective programming problems, Journal of Mathematical Analysis and Applications, 198 (1996), 621-635. https://doi.org/10.1006/jmaa.1996.0103
  14. J. Zhang and B. Mond, Duality for a non-differentiable programming problem, Bull. Austral. Math. Soc Vol. 55 (1997) 29-44. https://doi.org/10.1017/S0004972700030513