  Under study are some vector optimization problems over the space of Minkowski
balls, i.e., symmetric convex compact subsets in Euclidean space. A typical
problem requires to achieve the best result in the presence of conflicting
goals; e.g., given the surface area of a symmetric convex body $\mathfrak x$,
we try to maximize the volume of $\mathfrak x$ and minimize the width of
$\mathfrak x$ simultaneously.
