This paper studies the representation of a non-negative polynomial f on a non-compact semi-algebraic set K modulo its KKT (Karush-Kuhn-Tucker) ideal. Under the assumption that f satisfies the boundary Hessian conditions (BHC) at each zero of f in K, we show that f can be represented as a sum of squares (SOS) of real polynomials modulo its KKT ideal if f ≥ 0 on K.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap102-2-1,
author = {Dang Tuan Hiep},
title = {Representations of non-negative polynomials via KKT ideals},
journal = {Annales Polonici Mathematici},
volume = {101},
year = {2011},
pages = {101-109},
zbl = {1268.14051},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap102-2-1}
}
Dang Tuan Hiep. Representations of non-negative polynomials via KKT ideals. Annales Polonici Mathematici, Tome 101 (2011) pp. 101-109. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap102-2-1/