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(F, ρ)-invexity of higher order for multiobjective fractional variational problem

Kumar P., Sharma B.

Control and Cybernetics

2018

Vol. 47, no. 2

131--146

Multiobjective fractional variational problem is considered and suﬃcient optimality conditions, characterizing eﬃciency of higher order, are obtained under the assumptions of (F,ρ)−invexity of higher order on the functionals involved. Parametric higher order dual of the above stated problem is proposed. Duality theorems are proved to relate eﬃcient solutions of higher order for primal and its dual problem using generalized class of functionals.

Higher order eﬃciency and duality for multiobjective variational problem

Kumar P., Sharma B.

Control and Cybernetics

2017

Vol. 46, no. 2

137--145

In this paper, multiobjective variational programming problem is considered. Mond-Weir type higher order duality results are established by using the eﬃciency of higher order as the optimization tool. In order to prove these results, we propose the notion of generalized higher order (F,ρ,θ,m,h)−invexity.