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We give an algorithm which, up to some regularity assumptions on $\\F$, computes an exact representation of the global infimum $f^\\star=\\inf_{x\\in V\\cap\\R^n} f\\Par{x}$, i.e. a univariate polynomial vanishing at $f^\\star$ and an isolating interval for $f^\\star$. Furthermore, this algorithm decides whether $f^\\star$ is reached and if so, it returns $x^\\star\\in V\\cap\\R^n$ such that $f\\Pa"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1307.8281","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2013-07-31T11:01:20Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"ea0d66672013972ea0e46387a4f36a77b7f98b2e25a62c1c1a86c501b67edd1d","abstract_canon_sha256":"2c402449979c0bd6bd34da8770a5df8af22b3962df4c7063fc9e256a7cb47e2d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:52:32.360251Z","signature_b64":"Vtc85DKr31X1ARWKjd4MtE5FfWVb0Q5Rv1Zn+GvhR3Vum9oUflH+ndzj7R9b7pMvVzrG1PyUGK7BW8eYzasgDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1497766e23fc285aa1867cb6d9f7ec27b40d7b27c193e2ab8256f0afd29dbf21","last_reissued_at":"2026-05-18T02:52:32.359697Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:52:32.359697Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Probabilistic Algorithm for Polynomial Optimization over a Real Algebraic Set","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"cs.SC","authors_text":"Aur\\'elien Greuet (INRIA Paris-Rocquencourt, LIFL), LIP6, LIP6), LM-Versailles, Mohab Safey El Din (INRIA Paris-Rocquencourt","submitted_at":"2013-07-31T11:01:20Z","abstract_excerpt":"Let $f, f_1, \\ldots, f_\\nV$ be polynomials with rational coefficients in the indeterminates $\\bfX=X_1, \\ldots, X_n$ of maximum degree $D$ and $V$ be the set of common complex solutions of $\\F=(f_1,\\ldots, f_\\nV)$. We give an algorithm which, up to some regularity assumptions on $\\F$, computes an exact representation of the global infimum $f^\\star=\\inf_{x\\in V\\cap\\R^n} f\\Par{x}$, i.e. a univariate polynomial vanishing at $f^\\star$ and an isolating interval for $f^\\star$. 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