论文标题
在牛顿 - 多层型充足条件下，多项式的强制性
On Newton-polytope-type sufficiency conditions for coercivity of polynomials
论文作者
论文摘要
我们确定了新的充足条件，以使一般多元多项式的强制性$ f \ in \ mathbb {r} [x] $在无穷大的Newton多型中表达，并且由多项式系数空间中的仿射线性不平等系统组成。通过锐化一类GEM不规则多项式的已经存在的必要条件，我们提供了电路多项式的强制性的表征，这扩展了这一经过良好研究的多项式类别的已知结果。对于已经存在的充分性条件，该条件包含涉及设定投影操作的描述，我们确定了涉及单个posynomial不平等的等效描述。这使它们更容易应用，因此从实际角度来看也更具吸引力。我们将结果与现有文献联系起来，并通过几个示例来说明结果。
We identify new sufficiency conditions for coercivity of general multivariate polynomials $f\in\mathbb{R}[x]$ which are expressed in terms of their Newton polytopes at infinity and which consist of a system of affine-linear inequalities in the space of polynomial coefficients. By sharpening the already existing necessary conditions for coercivity for a class of gem irregular polynomials we provide a characterization of coercivity of circuit polynomials, which extends the known results on this well studied class of polynomials. For the already existing sufficiency conditions for coercivity which contain a description involving a set projection operation, we identify an equivalent description involving a single posynomial inequality. This makes them more easy to apply and hence also more appealing from the practical perspective. We relate our results to the existing literature and we illustrate our results with several examples.
