Minkowski center – Optimization Online

Symmetry-dependence in Rounding of a Convex Body

Published: 2026/08/31

Convex Optimization, Linear, Cone and Semidefinite Programming, Polyhedra john ellipsoid, lowner ellipsoid, Minkowski center, rounding, symmetry

The symmetry measure of a convex body \(S\subset\mathbb{R}^n\) is given by: \[ \mathrm{sym}(S):=\max\{\alpha\ge0:\text{ there exists }x\in S\text{ such that } -\alpha(S-x)\subseteq S-x\}\,, \]where such an \(x\) is called a Minkowski center. We prove that every convex body \(S\) admits a \(\sqrt{\frac{n}{\mathrm{sym}(S)}}\)-rounding of \(S\), namely, there exists an origin-centered ellipsoid \(E\) and a center \(c\) such … Read more

Minkowski Centers via Robust Optimization: Computation and Applications

Published: 2022/01/19, Updated: 2024/12/19

Robust Optimization algorithmic convergence, geometry, Minkowski center, robust optimization

Centers of convex sets are geometric objects that have received extensive attention in the mathematical and optimization literature, both from a theoretical and practical standpoint. For instance, they serve as initialization points for many algorithms such as interior-point, hit-and-run, or cutting-planes methods. First, we observe that computing a Minkowski center of a convex set can be formulated as … Read more