论文标题
常规基因座密度下的奇异品种的nichtnegativstellensatz
A Nichtnegativstellensatz on singular varieties under the denseness of regular loci
论文作者
论文摘要
让$ v $是带有奇异性的真正代数品种，而$ f $是$ v $上的真正多项式非负。假设$ v $的常规基因座在$ v $中是通常的拓扑。利用Hironaka的奇异性解决方案和Demmel（Nie- Powers的Nichtnegativstellensatz），我们获得了基于正方形的代表，这些表示的总和表征了$ v $上的$ f $的非负性。这种表示使我们能够为多项式优化问题建立精确的半决赛松弛，其最佳解决方案可能是约束集的奇异性。
Let $V$ be a real algebraic variety with singularities and $f$ be a real polynomial non-negative on $V$. Assume that the regular locus of $V$ is dense in $V$ by the usual topology. Using Hironaka's resolution of singularities and Demmel--Nie--Powers' Nichtnegativstellensatz, we obtain a sum of squares-based representation that characterizes the non-negativity of $f$ on $V$. This representation allows us to build up exact semidefinite relaxations for polynomial optimization problems whose optimal solutions are possibly singularities of the constraint sets.
