Mixed Type Symmetric and Self Duality for Multiobjective Variational Problems

In this paper, a new formulation of multiobjective symmetric dual pair, called mixed type multiobjective symmetric dual pair, for multiobjective variational problems is presented. This mixed formulation unifies two existing Wolfe and Mond-Weir type symmetric dual pairs of multiobjective variational problems. For this pair of mixed type multiobjective variational problems, various duality theorems are established under invexity-incavity and pseudoinvexity-pseudoincavity of kernel functions appearing in the problems. Under additional hypotheses, a self duality theorem is validated. It is also pointed that our duality theorems can be viewed as dynamic generalization of the corresponding (static) symmetric and self duality of multiobjective nonlinear programming already existing in the literature.