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

摘要

We consider the problem of computing the minimum of a polynomial function gon a basic closed semialgebraic set E in R^n. We present a probabilisticsymbolic 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 andhas at least one compact connected component.