  This paper is a review of results on Optimisation which are perhaps not so
standard in the PDE realm. To this end, we consider the problem of deriving the
PDEs associated to the optimal control of a system of either ODEs or SDEs with
respect to a vector-valued cost functional. Optimisation is considered with
respect to a partial ordering generated by a given cone. Since in the vector
case minima may not exist, we define vectorial value functions as (Pareto)
minimals of the ordering. Our main objective is the derivation of the model
PDEs which turn out to be parametric families of HJB single equations instead
of systems of PDEs. However, this allows the use of the theory of Viscosity
Solutions.
