Multiple criteria problems over Minkowski balls

Abstract

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.