A Probabilistic Symbolic Algorithm to Find the Minimum of a Polynomial Function on a Basic Closed Semialgebraic Set

Abstract

We consider the problem of computing the minimum of a polynomial function g on a basic closed semialgebraic set (Formula presented.). We present a probabilistic symbolic algorithm to find a finite set of sample points of the subset (Formula presented.) where the minimum of g is attained, provided that (Formula presented.) is non-empty and has at least one compact connected component.