On the local stability of semidefinite relaxations
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10107_2021_1696_ReferencePDF.pdf
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Author(s)
Cifuentes, Diego
Agarwal, Sameer
Parrilo, Pablo A.
Thomas, Rekha R.
Date Issued
September 3, 2021
Publisher
Springer Berlin Heidelberg
Citation
Cifuentes, Diego, Agarwal, Sameer, Parrilo, Pablo A. and Thomas, Rekha R. 2021. "On the local stability of semidefinite relaxations."
Version
Author's final manuscript
Abstract
Abstract
We consider a parametric family of quadratically constrained quadratic programs and their associated semidefinite programming (SDP) relaxations. Given a nominal value of the parameter at which the SDP relaxation is exact, we study conditions (and quantitative bounds) under which the relaxation will continue to be exact as the parameter moves in a neighborhood around the nominal value. Our framework captures a wide array of statistical estimation problems including tensor principal component analysis, rotation synchronization, orthogonal Procrustes, camera triangulation and resectioning, essential matrix estimation, system identification, and approximate GCD. Our results can also be used to analyze the stability of SOS relaxations of general polynomial optimization problems.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International
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DOI of Published Version
https://doi.org/10.1007/s10107-021-01696-1
