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arXiv · 2211.12440

A Nichtnegativstellensatz on singular varieties under the denseness of regular loci

Ngoc Hoang Anh Mai
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Abstract

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.

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Ngoc Hoang Anh Mai. 2022-11-22. A Nichtnegativstellensatz on singular varieties under the denseness of regular loci. https://arxiv.org/abs/2211.12440

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