# Tightness of the semidefinite relaxation for orthogonal trace-sum maximization

arXiv: https://arxiv.org/abs/1911.08700 · HTML: https://mlsanity.com/paper/1911.08700/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Nov 2019.

## Built on by (most cited first, 1 of 1)

- [Orthogonal Group Synchronization with Incomplete Measurements: Error Bounds and Linear Convergence of the Generalized Power Method](https://mlsanity.com/paper/2112.06556/) (2021)

## Abstract (arXiv)

This paper studies an optimization problem on the sum of traces of matrix quadratic forms on m orthogonal matrices, which can be considered as a generalization of the synchronization of rotations. While the problem is nonconvex, the paper shows that its semidefinite programming relaxation can solve the original nonconvex problems exactly, under an additive noise model with small noise in the order of O(-m1/4), where m is the number of orthogonal matrices. This result can be considered as a generalization of existing results on phase synchronization.