On the minimum of a polynomial function on a basic closed semialgebraic set and applications

2011/12/02 by Gabriela Jeronimo, Jeronimo, Gabriela, Daniel Perrucci +3 · 1 citation
Computer Science · Mathematics · #Advanced Differential Equations and Dynamical Systems #Advanced Optimization Algorithms Research #Algebraic Geometry (math.AG) #Computational Geometry (cs.CG) #FOS: Computer and information sciences #FOS: Mathematics #Polynomial and algebraic computation #cs.CG #math.AG

paper · pdf · doi:10.48550/arxiv.1112.0544

arxiv created 2011/12/02 · openalex publication_date 2011/12/02 · arxiv updated 2011/12/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give an explicit upper bound for the algebraic degree and an explicit lower bound for the absolute value of the minimum of a polynomial function on a compact connected component of a basic closed semialgebraic set when this minimum is not zero. As an application, we obtain a lower bound for the separation of two disjoint connected components of basic closed semialgebraic sets, when at least one of them is compact.

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