Optimality Conditions and Second-Order Duality for Nondifferentiable Multiobjective Continuous Programming Problems
- 1 Department of Mathematics, Jaypee University of Engineering and Technology, Guna (M.P.), India
- 2 Department of Mathematics, Jaypee University of Engineering and Technology, Guna (M.P.), India
Abstract
Fritz John and Karush-Kuhn-Tucker type optimality conditions for a nondifferentiable multiobjective variational problem are derived. As an application of Karush-Kuhn-Tucker type optimality conditions, Mond-weir type second-order nondifferentiable multiobjective dual variational problems is constructed. Various duality results for the pair of Mond-Weir type second-order dual variational problems are proved under second-order pseudoinvexity and second-order quasi-invexity. A pair of Mond-Weir type dual variational problems with natural boundary values is formulated to derive various duality results. Finally, it is pointed out that our results can be considered as dynamic generalizations of their static counterparts existing in the literature.
- X. H. Chen, “Second Order Duality for the Variational Problems,” Journal of Mathematical Analysis and Applications, Vol. 286, No. 1, 2003, pp. 261-270. doi:10.1016/S0022-247X(03)00481-5
- I. Husain, “A. Ahmed and Mashoob Masoodi,” European Journal of Pure and Applied Mathematics, Vol. 2, No. 2 2009, pp. 278-295.
- I. Husain and M. Masoodi, “Second-Order Duality for a Class of Nondifferentiable Continuous Programming Problems,” European Journal of Pure and Applied Mathematics, Vol. 5, No. 3, 2012, pp. 390-400.
- I. Husain and S. K. Srivastav, “On Second-Order Duality in Nondifferentiable Continuous Programming,” American Journal of Operations Research, Vol. 2, No. 3, 2012, pp. 289-295.
- V. Chankong and Y. Y. Haimes, “Multiobjective Decision Making Theory and Methodology,” North-Holland, New York, 1983.
- S. Chandra, B. D. Craven and I. Husain, “A Class of Nondifferentiable Continuous Programming Problem,” Journal of Mathematical Analysis and Applications, Vol. 107, No. 1, 1985, pp. 122-131. doi:10.1016/0022-247X(85)90357-9