Duality in vector optimization via augmented Lagrangian

This paper is devoted to developing augmented Lagrangian duality theory in vector optimization. By using the concepts of the supremum and infimum of a set and conjugate duality of a set-valued map on the basic of weak efficiency, we establish the interchange rules for a set-valued map, and propose an augmented Lagrangian function for a vector optimization problem with set-valued data. Under this augmented Lagrangian, weak and strong duality results are given. Then we derive sufficient conditions for penalty representations of the primal problem. The obtained results extend the corresponding theorems existing in scalar optimization.