An analysis of some dual problems in multiobjective optimization (I)

In this work we study the duality for a general multiobjective optimization problem. Considering first, a scalar problem, different duals using the conjugacy approach are presented. Starting from these scalar duals, we introduce six different multiobjective dual problems to the primal one, one depending on certain vector parameters. The existence of weak and, under certain conditions, strong duality between the primal and the dual problems is shown. Afterwards, some inclusion results for the image sets of the multiobjective dual problems (D1), (Da) and (DFL) are derived. Moreover, we verify that the efficiency sets within the image sets of these problems coincide, but the image sets themselves do not.