{"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 $f^\\star$. 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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.8281","kind":"arxiv","version":2},"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"}