A probabilistic symbolic algorithm to find the minimum of a polynomial function on a basic closed semialgebraic set

We consider the problem of computing the minimum of a polynomial function g on a basic closed semialgebraic set E in R^n. We present a probabilistic symbolic algorithm to find a finite set of sample points of the subset E^{min} of E where the minimum of g is attained, provided that E^{min} is non-empty and has at least one compact connected component.