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• W3177276558 abstract "We provide the following generalization of the Löwner-John's ellipsoid theorem. Given a (non necessarily convex) compact set K ⊂ ℝ <sup xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>n</sup> and an even integer d ∈ ℕ, there is a unique homogeneous polynomial g of degree d such that K ⊂ G := {x : g(x) ≤ 1} and G has minimum volume among all such sets. The symmetric case of the Lowner-John theorem is a particular case when d = 2, and importantly, we neither require the set K nor the sublevel set G to be convex. We also provide a numerical scheme to approximate the optimal value and the unique optimal solution as closely as desired." @default.
• W3177276558 created "2021-07-05" @default.
• W3177276558 creator A5006670993 @default.
• W3177276558 date "2013-12-01" @default.
• W3177276558 modified "2023-09-30" @default.
• W3177276558 title "A generalization of the L&#x00F6;wner-John's ellipsoid theorem" @default.
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• W3177276558 doi "https://doi.org/10.1109/cdc.2013.6759917" @default.
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