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On an extension of Pólya’s Positivstellensatz. (English) Zbl 1379.11037
Summary: In this paper, we provide a generalization of a Positivstellensatz by G. Pólya [Vierteljahrsschrift Zürich 73, 141–145 (1928; JFM 54.0138.01)]. We show that if a homogeneous polynomial is positive over the intersection of the non-negative orthant and a given basic semialgebraic cone (excluding the origin), then there exists a “Pólya type” certificate for non-negativity. The proof of this result uses the original Positivstellensatz by Pólya, and a Positivstellensatz by M. Putinar and F.-H. Vasilescu [C. R. Acad. Sci., Paris, Sér. I, Math. 328, No. 7, 585–589 (1999; Zbl 0973.14031)].

##### MSC:
 11E25 Sums of squares and representations by other particular quadratic forms 14P05 Real algebraic sets 14P10 Semialgebraic sets and related spaces 90C30 Nonlinear programming
##### Software:
CPLEX; Mosek; Decision tree for optimization software
Full Text:
##### References:
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