Duality for Non-differentiable Multi-objective Fractional Variational Problem

In this paper, we have introduced efficiency of order m for a class of non-differentiable multi-objective variational problems in which every component of the objective and constraint function contains a term involving the square root of a certain positive semidefinite quadratic form. necessary optimality conditions are obtained for this solution concept. parametric dual of non-differentiable multi-objective fractional variational problem is proposed. duality theorems are proved to relate efficient solutions of order m for primal problem and its dual. these results are obtained using generalized ρ−invex functionals of order m. proposed notion of efficiency of order m leads to stronger results whereas ρ−invexity of higher order broadens the domain of the problem.