On the Minimum of a Polynomial Function on a Basic Closed Semialgebraic Set and Applications
Gabriela Jeronimo, Daniel Perrucci, Elias Tsigaridas · SIAM Journal on Optimization · 2013
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 noncompact 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.