Dehomogenization for Completely Positive Tensors
Jiawang Nie, Xindong Tang, Zi Yang, Suhan Zhong
TL;DR
This paper introduces a dehomogenization method for completely positive tensors, leading to improved Moment-SOS relaxations and more efficient detection and optimization within CP tensor cones.
Contribution
The paper presents a novel dehomogenization approach that enhances the analysis and optimization of completely positive tensors, providing new relaxations and computational efficiencies.
Findings
Enhanced Moment-SOS relaxations for CP tensors
More efficient detection of CP tensors
Improved linear conic optimization with CP tensor cones
Abstract
A real symmetric tensor is completely positive (CP) if it is a sum of symmetric tensor powers of nonnegative vectors. We propose a dehomogenization approach for studying CP tensors. This gives new Moment-SOS relaxations for CP tensors. Detection for CP tensors and the linear conic optimization with CP tensor cones can be solved more efficiently by the dehomogenization approach.
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Taxonomy
TopicsTensor decomposition and applications · Computational Physics and Python Applications