Maximizing products of linear forms, and the permanent of positive semidefinite matrices
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10107_2021_1616_ReferencePDF.pdf
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Author(s)
Yuan, Chenyang
Parrilo, Pablo A.
Date Issued
January 18, 2021
Publisher
Springer Berlin Heidelberg
Citation
Yuan, Chenyang and Parrilo, Pablo A. 2021. "Maximizing products of linear forms, and the permanent of positive semidefinite matrices."
Version
Author's final manuscript
Abstract
Abstract
We study the convex relaxation of a polynomial optimization problem, maximizing a product of linear forms over the complex sphere. We show that this convex program is also a relaxation of the permanent of Hermitian positive semidefinite (HPSD) matrices. By analyzing a constructive randomized rounding algorithm, we obtain an improved multiplicative approximation factor to the permanent of HPSD matrices, as well as computationally efficient certificates for this approximation. We also propose an analog of van der Waerden’s conjecture for HPSD matrices, where the polynomial optimization problem is interpreted as a relaxation of the permanent.
MIT Department
Massachusetts Institute of Technology. Laboratory for Information and Decision Systems
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1007/s10107-021-01616-3
