Discriminants and Nonnegative Polynomials

Details Discriminants and Nonnegative Polynomials Discriminants and Nonnegative Polynomials

2010-02-10

arxiv.org/abs/1002.2230v2

Mathematics

Optimization and Control

31 pages, 5 figures

Scientific paper

For a semialgebraic set K in R^n, let P_d(K) be the cone of polynomials in R^n of degrees at most d that are nonnegative on K. This paper studies the geometry of its boundary. When K=R^n and d is even, we show that its boundary lies on the irreducible hypersurface defined by the discriminant of a single polynomial. When K is a real algebraic variety, we show that P_d(K) lies on the hypersurface defined by the discriminant of several polynomials. When K is a general semialgebraic set, we show that P_d(K) lies on a union of hypersurfaces defined by the discriminantal equations. Explicit formulae for the degrees of these hypersurfaces and discriminants are given. We also prove that typically P_d(K) does not have a log-polynomial type barrier, but a log-semialgebraic type barrier exits. Some illustrating examples are shown.

Affiliated with

Also associated with

No associations

Rating

Discriminants and Nonnegative Polynomials does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Discriminants and Nonnegative Polynomials, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Discriminants and Nonnegative Polynomials will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-67742