Maximizing Products of Linear Forms, and The Permanent of Positive Semidefinite Matrices release_ra37myimgrfn3e5ro5iqqqonrq

by Chenyang Yuan, Pablo A. Parrilo

Released as a article .

2021  

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.
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Type  article
Stage   submitted
Date   2021-01-13
Version   v2
Language   en ?
arXiv  2002.04149v2
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