Moment-SOS relaxations for moment and tensor recovery problems
Lei Huang, Jiawang Nie, Jiajia Wang
TL;DR
This paper introduces Moment-SOS relaxations for efficiently recovering moments and tensors within semialgebraic sets, demonstrating broad applications and numerical effectiveness in tensor decomposition problems.
Contribution
The paper develops a novel Moment-SOS relaxation framework tailored for moment and tensor recovery problems with low decomposition rank.
Findings
Effective recovery of moments and tensors demonstrated
Numerical experiments confirm efficiency and broad applicability
Applicable to various tensor decomposition scenarios
Abstract
This paper studies moment and tensor recovery problems whose decomposing vectors are contained in some given semialgebraic sets. We propose Moment-SOS relaxations with generic objectives for recovering moments and tensors, whose decomposition lengths are expected to be low. This kind of problems have broad applications in various tensor decomposition questions. Numerical experiments are provided to demonstrate the efficiency of this approach.
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Taxonomy
TopicsAdvanced Numerical Methods in Computational Mathematics · Matrix Theory and Algorithms · Elasticity and Material Modeling