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On the local stability of semidefinite relaxations

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arxiv 1710.04287 v4 pith:CCN2KLAD submitted 2017-10-11 math.OC math.AG

Diego Cifuentes , Sameer Agarwal , Pablo A. Parrilo , Rekha R. Thomas This is my paper · ORCID
classification math.OCmath.AG
keywords relaxationsestimationexactnominalparameterproblemsrelaxationsemidefinite
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We consider a parametric family of quadratically constrained quadratic programs (QCQP) 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.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Algebraic Representations for Volumetric Frame Fields

    cs.GR 2019-08 conditional novelty 8.0 of 10

    Octahedral frame space embeds isometrically in R9, giving closed-form geodesics and SDP projection, and a new odeco frame type handles singular curves.

  2. On computing the nonlinearity interval in parametric semidefinite optimization

    math.OC 2019-08 conditional novelty 6.0 of 10

    The authors show transition points in parametric semidefinite optimization are finite and give a numerical algebraic geometry algorithm to find nonlinearity intervals and transition points.

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