{"ID":2921923,"CreatedAt":"2026-06-02T02:42:49.606572591Z","UpdatedAt":"2026-06-04T00:54:56.190393508Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2606.01548","arxiv_id":"2606.01548","title":"Minimal intersection radius for $n$ growing, non-homogeneous ellipsoids in $\\mathbb{R}^d$","abstract":"In this paper, we compute the Minimal Intersection Radius (MIR) of growing, non-homogeneous ellipsoids in arbitrary ambient dimension. We provide a geometric method to find the MIR using techniques from convex optimization, a secondary method using second-order cone programs, and show that the MIR can be phrased as an LP-type problem, where the computation from convex optimization acts as a certificate. We implement these methods and benchmark them using different convex solvers, and with or without the LP setting. We also provide a comparison with similar but different problems that appeared in the literature, and show that finding the MIR is, in general, not equivalent to finding the minimal enclosing ellipsoid.","short_abstract":"In this paper, we compute the Minimal Intersection Radius (MIR) of growing, non-homogeneous ellipsoids in arbitrary ambient dimension. We provide a geometric method to find the MIR using techniques from convex optimization, a secondary method using second-order cone programs, and show that the MIR can be phrased as an...","url_abs":"https://arxiv.org/abs/2606.01548","url_pdf":"https://arxiv.org/pdf/2606.01548v1","authors":"[\"Barbara Giunti\",\"Sean Hill\",\"Felix X. -F. Ye\"]","published":"2026-06-01T01:48:05Z","proceeding":"math.OC","tasks":"[\"math.OC\",\"math.AT\"]","methods":"[]","has_code":false}