{"ID":2826012,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.20826","arxiv_id":"2512.20826","title":"Optimal Algorithms for Nonlinear Estimation with Convex Models","abstract":"A linear functional of an object from a convex symmetric set can be optimally estimated, in a worst-case sense, by a linear functional of observations made on the object. This well-known fact is extended here to a nonlinear setting: other simple functionals of the object can be optimally estimated by functionals of the observations that share a similar simple structure. This is established for the maximum of several linear functionals and even for the $\\ell$th largest among them. Proving the latter requires an unusual refinement of the analytical Hahn--Banach theorem. The existence results are accompanied by practical recipes relying on convex optimization to construct the desired functionals, thereby justifying the term of estimation algorithms.","short_abstract":"A linear functional of an object from a convex symmetric set can be optimally estimated, in a worst-case sense, by a linear functional of observations made on the object. This well-known fact is extended here to a nonlinear setting: other simple functionals of the object can be optimally estimated by functionals of the...","url_abs":"https://arxiv.org/abs/2512.20826","url_pdf":"https://arxiv.org/pdf/2512.20826v1","authors":"[\"Simon Foucart\"]","published":"2025-12-23T23:01:31Z","proceeding":"math.FA","tasks":"[\"math.FA\",\"math.OC\",\"math.ST\"]","methods":"[]","has_code":false}