Upper-semi-continuity and cone-concavity of multi-valued vector functions in a duality theory for vector optimization

Following a few words on multifunctions in the mathematical literature, a very brief recall on dual spaces, some preliminary notations and definitions in the introduction, we give some results on those functions in the second paragraph. In the third paragraph, a duality theory in cone-optimization involving multifunctions is developed with the concept of the strong instead of the weak cone-optimality criterion. The results so obtained account for existing ones on uni-vocal vector-function optimization and they hold in spaces of arbitrary dimension.