Optimization and equilibrium problems have been extensively studied when the involved preference relations admit a representation by means of realvalued functions. Although these problems have been analyzed under very minimal assumptions on the representation function, this context could appear to be quite restrictive in some practical situations. The aim of this talk is to present a new study of preference relations in topological spaces and to analyze, in Banach spaces, a suitable concept of a normal operator to upper contour set. In doing this, we propose the concept of weak upper continuity for preference relations and we compare it with the other continuity-like notions available in the literature. As an application of our theoretical developments, we analyze a preference equilibrium problem by using a suitable quasi-variational inequality formulation: as an example, a preference allocation problem (possibly under time and uncertainty) is also considered.