{"paper":{"title":"Lower Bounds for a Polynomial on a basic closed semialgebraic set using geometric programming","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Mehdi Ghasemi, Murray Marshall","submitted_at":"2013-11-15T04:49:58Z","abstract_excerpt":"$f,g_1,...,g_m$ be elements of the polynomial ring $\\mathbb{R}[x_1,...,x_n]$. The paper deals with the general problem of computing a lower bound for $f$ on the subset of $\\mathbb{R}^n$ defined by the inequalities $g_i\\ge 0$, $i=1,...,m$. The paper shows that there is an algorithm for computing such a lower bound, based on geometric programming, which applies in a large number of cases. The algorithm extends and generalizes earlier algorithms of Ghasemi and Marshall, dealing with the case $m=0$, and of Ghasemi, Lasserre and Marshall, dealing with the case $m=1$ and $g_1= M-(x_1^d+\\cdots+x_n^d)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.3726","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"}