Weak efficiency of higher order for multiobjective fractional variational problem

Abstract

The notion of weak efficiency of higher order for multiobjective fractional variational problem has been introduced. Examples are presented to illustrate this new solution concept. ρ-invexity is extended to ρ-invexity of higher order. Four generalizations of ρ-invexity of higher order are given. It is shown with the help of examples that this new class of ρ-invex functionals of higher order is larger than the existing class of functionals. Sufficient optimality conditions are proved under newly defined generalized ρ−invexity assumptions on the functionals involved. Parametric dual for multiobjective fractional variational problem is proposed for which weak duality theorem is proved. Further, we introduce weighted variational parametric problem to prove strong duality theorem.