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SYMMETRIC DUALITY FOR FRACTIONAL VARIATIONAL PROBLEMS WITH CONE CONSTRAINTS
Ahmad, I.,Yaqub, Mohd.,Ahmed, A. 한국전산응용수학회 2007 Journal of applied mathematics & informatics Vol.23 No.1
A pair of symmetric fractional variational programming problems is formulated over cones. Weak, strong, converse and self duality theorems are discussed under pseudoinvexity. Static symmetric dual fractional programs are included as special case and corresponding symmetric duality results are merely stated.
Multiobjective fractional symmetric duality involving cones
I. Ahmad,Sarita Sharma 한국전산응용수학회 2008 Journal of applied mathematics & informatics Vol.26 No.1
A pair of multiobjective fractional symmetric dual programs is formulated over arbitrary cones. Weak, strong and converse duality theorems are proved under pseudoinvexity assumptions. A self duality theorem is also discussed.
MULTIOBJECTIVE FRACTIONAL SYMMETRIC DUALITY INVOLVING CONES
Ahmad, I.,Sharma, Sarita Korean Society of Computational and Applied Mathem 2008 Journal of applied mathematics & informatics Vol.26 No.1
A pair of multiobjective fractional symmetric dual programs is formulated over arbitrary cones. Weak, strong and converse duality theorems are proved under pseudoinvexity assumptions. A self duality theorem is also discussed.
Husain, I.,Ahmed, A.,Rumana, G. Mattoo The Korean Society for Computational and Applied M 2009 Journal of applied mathematics & informatics Vol.27 No.1
A multiobjective variational problem involving higher order derivatives is considered and Fritz-John and Karush-Kuhn-Tucker type optimality conditions for this problem are derived. As an application of Karush-Kuhn-Tucker optimality conditions, Wolfe type dual to this variational problem is constructed and various duality results are validated under generalized invexity. Some special cases are mentioned and it is also pointed out that our results can be considered as a dynamic generalization of the already existing results in nonlinear programming.
I. Husain,A. Ahmed,G. MATTOO 한국전산응용수학회 2009 Journal of applied mathematics & informatics Vol.27 No.1
A multiobjective variational problem involving higher order derivatives is considered and Fritz-John and Karush-Kuhn-Tucker type optimality conditions for this problem are derived. As an application of Karush-Kuhn-Tucker optimality conditions, Wolfe type dual to this variational problem is constructed and various duality results are validated under generalized invexity. Some special cases are mentioned and it is also pointed out that our results can be considered as a dynamic generalization of the already existing results in nonlinear programming. A multiobjective variational problem involving higher order derivatives is considered and Fritz-John and Karush-Kuhn-Tucker type optimality conditions for this problem are derived. As an application of Karush-Kuhn-Tucker optimality conditions, Wolfe type dual to this variational problem is constructed and various duality results are validated under generalized invexity. Some special cases are mentioned and it is also pointed out that our results can be considered as a dynamic generalization of the already existing results in nonlinear programming.
Mond-Weir Duality for Multiobjective Programming with Invexity
Xiuni Yang 보안공학연구지원센터 2015 International Journal of Hybrid Information Techno Vol.8 No.12
This paper deals with the duality for a class of multiobjective programming problems including inequality constraints. To establish and prove the dual results for the multiobjective programming problems, the dual models and the classes of generalized invexity functions so-called F J - d - αβ - Ρt - θ - pseudoinvex-I are introduced. Using the new concepts, the weak dual, strong dual and converse dual theorems are obtained for the multiobjective programming problems.
Efficiency in Multiobjective Programming with Generalized Invexity
Xiuni Yang 보안공학연구지원센터 2015 International Journal of u- and e- Service, Scienc Vol.8 No.11
This paper is concerned with the multiobjective programming problems including inequality constraints. By utilizing the directional derivatives in the direction η ( x , x ) , the new classes of generalized invexity functions are introduced. Using the new concepts, the sufficient optimality conditions are obtained. It is proved that the feasible solutions of the multiobjective programming problems are an efficient solution (or a weakly efficient solution) for the multiobjective programming problems.