{"paper":{"title":"H\\\"older-Type Global Error Bounds for Non-degenerate Polynomial Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Ha Huy Vui, Pham Tien Son, Si Tiep Dinh","submitted_at":"2014-11-04T10:57:47Z","abstract_excerpt":"Let $F := (f_1, \\ldots, f_p) \\colon {\\Bbb R}^n \\to {\\Bbb R}^p$ be a polynomial map, and suppose that $S := \\{x \\in {\\Bbb R}^n \\ : \\ f_i(x) \\le 0, i = 1, \\ldots, p\\} \\ne \\emptyset.$ Let $d := \\max_{i = 1, \\ldots, p} \\deg f_i$ and $\\mathcal{H}(d, n, p) := d(6d - 3)^{n + p - 1}.$ Under the assumption that the map $F \\colon {\\Bbb R}^n \\rightarrow {\\Bbb R}^p$ is convenient and non-degenerate at infinity, we show that there exists a constant $c > 0$ such that the following so-called {\\em H\\\"older-type global error bound result} holds $$c d(x,S) \\le [f(x)]_+^{\\frac{2}{\\mathcal{H}(2d, n, p)}} + [f(x)]"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.0859","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}