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

Gabriella Jeronimo (1) , Daniel Perrucci (1) , Elias Tsigaridas (2)

1 Departamento de Matemática [Buenos Aires]
2 PolSys - Polynomial Systems

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. We also present extensions of these results to non-compact situations. 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.

Domaines: Calcul formel [cs.SC]

Gabriella Jeronimo, Daniel Perrucci, Elias Tsigaridas. On the minimum of a polynomial function on a basic closed semialgebraic set and applications. SIAM Journal on Optimization, 2013, 23 (1), pp.241--255. ⟨hal-00776280v2⟩