The positive semi-definite cone and sum-of-squares cone of Hankel form

Zhongming Chen; Liqun Qi

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arXiv · 1505.03201

The positive semi-definite cone and sum-of-squares cone of Hankel form

Zhongming Chen·Liqun Qi

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Abstract

In this paper, the geometry properties of Hankel form are studied, including their positive semi-definite (PSD) cone and sum-of-squares (SOS) cone. We denote them by $HPSD(m,n)$ and $HSOS(m,n)$, respectively. We show that both $HPSD(m,n)$ and $HSOS(m,n)$ are closed convex cones. The dual cone of $HPSD(m,n)$ is the convex hull of all $m$-times convolutions of real vectors. Besides, we derive the dual cone of SOS tensors. By reformulation, it follows that the dual cone of $HSOS(m,n)$ can also be written explicitly. These results may lead further research on the Hilbert-Hankel problem.

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BibTeX RIS

Zhongming Chen, Liqun Qi. 2015-05-13. The positive semi-definite cone and sum-of-squares cone of Hankel form. https://arxiv.org/abs/1505.03201

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