In this article we develop a new approach to duality theory for convex vector optimization problems. We modify a given (set-valued) vector optimization problem such that the image space becomes a complete lattice (a sublattice of the power set of the original image space), where the corresponding infimum and supremum are sets that are related to the set of (minimal and maximal) weakly efficient...

Duality, which relates the strongly coupled behavior of one gauge theory to the weakly coupled behavior of another, has emerged as a key idea in the understanding of the nonperturbative dynamics of supersymmetric gauge theories. Most of the work in this context has focused on gauge theories with simple gauge groups. One would like to understand theories with non-simple groups in more detail: i....