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

2015/05/13 by Zhongming Chen, Liqun Qi, Chen, Zhongming +1
Computer Science · Engineering · Mathematics · #Elasticity and Material Modeling #FOS: Mathematics #Matrix Theory and Algorithms #Spectral Theory (math.SP) #Tensor decomposition and applications #math.SP

paper · pdf · doi:10.48550/arxiv.1505.03201

openalex publication_date 2015/05/13 · arxiv created 2015/05/16 · arxiv updated 2015/05/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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