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.

8 pages. arXiv admin note: substantial text overlap with arXiv:1208.6507