Duality for vector optimization problems via a general scalarization

Abstract

Considering a vector optimization problem to which properly efficient solutions are defined by using convex cone-monotone scalarization functions, we attach to it, by means of perturbation theory, new vector duals. When the primal problem, the scalarization function and the perturbation function are particularized, different dual vector problems are obtained, some of them are already known in the literature. Weak and strong duality statements are delivered in each case.

Keywords:

• vector duality
• conjugate functions
• cone-monotone functions
• cones

AMS Subject Classifications:

• 49N15
• 90C25
• 90C29

Acknowledgements

This research was partially supported by DFG (German Research Foundation), project WA 922/1-3.