Generalized (F,ρ)-Convexity and Duality in Nonsmooth Problems of Multiobjective Optimization

A mixed-type dual for a nonsmooth multiobjective optimization problem with inequality and equality constraints is formulated. We obtain weak and strong duality theorems for a mixed-type dual without requiring the regularity assumptions and the nonnegativeness of the Lagrange multipliers associated to the equality constraints. We apply also a nonsmooth constraint qualification for multiobjective programming to establish strong duality results. In this case, our constraint qualification assures the existence of positive Lagrange multipliers associated with the vector-valued objective function.