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

TL;DR

This paper introduces a probabilistic symbolic algorithm designed to find sample points where a polynomial function attains its minimum on a specific semialgebraic set, under certain conditions.

Contribution

It proposes a novel probabilistic symbolic method for locating points of minimum on semialgebraic sets, enhancing computational approaches in polynomial optimization.

Findings

Algorithm successfully finds sample points where the minimum is attained.

Applicable when the minimum set has at least one compact connected component.

Provides a finite set of points representing the minimum locations.

Abstract

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.