Abstract: In this paper, the author introduces a generalized augmented Lagrangian for minimizing an extended vector-valued function. Based on the generalized augmented Lagrangian, the author constructs set-valued dual functions and dual optimization problems, obtain weak and strong duality results without any convexity required, apply the results for solving a constrained vector optimization problem. The results improve and generalize some known results.

Key words: Generalized augmented Lagrangian, Strong duality, Weak duality, Constrained vector optimization problem