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On geodesically convex formulations for the brascamp-lieb constant
Name
LIPIcs-APPROX-RANDOM-2018-25.pdf
Description
Published version
Size
424.78 KB
Format
Adobe PDF
Checksum (MD5)
f7e5b09137d523341b009709db8c9dd2
Date Issued
April 2018
Journal
Leibniz International Proceedings in Informatics, LIPIcs
Citation
2018. "On geodesically convex formulations for the brascamp-lieb constant." Leibniz International Proceedings in Informatics, LIPIcs, 116.
Version
Final published version
Abstract
© 2018 Aditya Bhaskara and Srivatsan Kumar. We consider two non-convex formulations for computing the optimal constant in the Brascamp-Lieb inequality corresponding to a given datum and show that they are geodesically log-concave on the manifold of positive definite matrices endowed with the Riemannian metric corresponding to the Hessian of the log-determinant function. The first formulation is present in the work of Lieb [15] and the second is new and inspired by the work of Bennett et al. [5]. Recent work of Garg et al. [12] also implies a geodesically log-concave formulation of the Brascamp-Lieb constant through a reduction to the operator scaling problem. However, the dimension of the arising optimization problem in their reduction depends exponentially on the number of bits needed to describe the Brascamp-Lieb datum. The formulations presented here have dimensions that are polynomial in the bit complexity of the input datum.
Terms of Use
Creative Commons Attribution 4.0 International license
Persistent DSpace Link
DOI of Published Version
10.4230/LIPIcs.APPROX-RANDOM.2018.25
