Minimal intersection radius for $n$ growing, non-homogeneous ellipsoids in $\mathbb{R}^d$
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866911739153481728 |
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| author | Giunti, Barbara Hill, Sean Ye, Felix X. -F. |
| author_facet | Giunti, Barbara Hill, Sean Ye, Felix X. -F. |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2606_01548 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Minimal intersection radius for $n$ growing, non-homogeneous ellipsoids in $\mathbb{R}^d$ Giunti, Barbara Hill, Sean Ye, Felix X. -F. Optimization and Control Algebraic Topology 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. |
| title | Minimal intersection radius for $n$ growing, non-homogeneous ellipsoids in $\mathbb{R}^d$ |
| topic | Optimization and Control Algebraic Topology |
| url | https://arxiv.org/abs/2606.01548 |