Duality for Multiobjective Variational Control and Multiobjective Fractional Variational Control Problems with Pseudoinvexity

The relationship between mathematical programming and classical calculus of variation was explored and extended by Hanson [6]. Thereafter variational programming problems have attracted some attention in literature. Duality for multiobjective variational problems has been of much interest in the recent years, and several contributions have been made to its development (see, e.g., Bector and Husain [2], Nahak and Nanda [9], Mishra and Mukherjee [7]). Using parametric equivalence, Bector et al. [1] formulated a dual program for a multiobjective fractional program involving continuously differentiable convex functions. Recently Nahak and Nanda [10] proved the duality theorems of multiobjective variational control problems under (F,ρ)-convexity assumptions. In this paper, under pseudoinvexity assumptions on the functions involved, duality theorems are proved for multiobjective variational control problems. The duality of multiobjective fractional variational control problems is also considered by relating the primal problem to a parametric multiobjective variational control problem.