Representations of non-negative polynomials via KKT ideals

• Autorzy: Dang Tuan Hiep
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 13P25: Applications of commutative algebra (e.g., to statistics, control theory, optimization, etc.)
• 90C22: Semidefinite programming
• 11E25: Sums of squares and representations by other particular quadratic forms
• 14P10: Semialgebraic sets and related spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2011
• Tom: 102
• Numer: 2
• Strony: 101-109

Daty

wydano

2011

Twórcy

autor

Dang Tuan Hiep

• Department of Mathematics, University of Dalat, 01 Phu Dong Thien Vuong, Da Lat, Vietnam
• Dipartimento di Matematica, Università degli Studi di Bari Aldo Moro, Via E. Orabona, 4, 70125 Bari, Italy

Identyfikatory

DOI

10.4064/ap102-2-1