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Systems of polynomials with at least one positive real zero. (English) Zbl 1491.12001

Summary: In this paper, we prove several theorems on systems of polynomials with at least one positive real zero based on the theory of coercive polynomials. These theorems provide sufficient conditions for systems of multivariate polynomials admitting at least one positive real zero in terms of their Newton polytopes and combinatorial structure. Moreover, a class of polynomials attaining their global minimums in the first quadrant are given, which is useful in polynomial optimization.

MSC:

12D10 Polynomials in real and complex fields: location of zeros (algebraic theorems)
13J30 Real algebra
14P10 Semialgebraic sets and related spaces
90C23 Polynomial optimization
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