论文标题
时刻，正方和热带化的总和
Moments, Sums of Squares, and Tropicalization
论文作者
论文摘要
我们使用热带化来研究双重多项式和正方形的双锥上的双锥，并在半格式集合$ s $上进行。 $ s $上支持的$ S $支撑的措施的截断锥对$ s $双重双重，而“伪派”对非负多项式的正方形近似值是双重的。我们提供了当时和伪时锥的热带化的明确组合描述，并证明了它们在区分非负多项式和正方形总和时的有用性。我们提供的例子显示了非负多项式的正方形近似值的新局限性。如果通过二项式不等式定义了半格式集合，则其力矩和伪矩锥体在Hadamard产品下关闭。在这种情况下，它们的热带化是多面体锥，它们在瞬间和伪矩锥上编码所有二项式不平等。
We use tropicalization to study the duals to cones of nonnegative polynomials and sums of squares on a semialgebraic set $S$. The truncated cones of moments of measures supported on the set $S$ is dual to nonnegative polynomials on $S$, while "pseudo-moments" are dual to sums of squares approximations to nonnegative polynomials. We provide explicit combinatorial descriptions of tropicalizations of the moment and pseudo-moment cones, and demonstrate their usefulness in distinguishing between nonnegative polynomials and sums of squares. We give examples that show new limitations of sums of squares approximations of nonnegative polynomials. When the semialgebraic set is defined by binomial inequalites, its moment and pseuo-moment cones are closed under Hadamard product. In this case, their tropicalizations are polyhedral cones that encode all binomial inequalities on the moment and pseudo-moment cones.
