Mixed type duality for multiobjective variational problems

Abstract

The concept of mixed-type duality has been extended to the class of multiobjective variational problems. A number of duality relations are proved to relate the efficient solutions of the primal and its mixed-type dual problems. The results are obtained for ρ-convex (generalized ρ-convex) functions. These studies have been generalized to the case of ρ-invex (generalized ρ-invex) functions. Our results apparently generalize a fairly large number of duality results previously obtained for finite-dimensional nonlinear programming problems under various convexity assumptions.