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On the multiobjective control problem

Kumar P., Sharma B.

Journal of Applied Analysis

2018

Vol. 24, nr 2

223--231

In this paper, sufficient optimality conditions are established for the multiobjective control problem using efficiency of higher order as a criterion for optimality. The ρ-type 1 invex functionals (taken in pair) of higher order are proposed for the continuous case. Existence of such functionals is confirmed by a numer of examples. It is shown with the help of an example that this class is more general than the existing class of functionals.Weak and strong duality theorems are also derived for a mixed dual in order to relate efficient solutions of higher order for primal and dual problems.

(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.