Logo TIB AV-Portal Logo TIB AV-Portal

Rank optimality for the Burer-Monteiro factorization

Video in TIB AV-Portal: Rank optimality for the Burer-Monteiro factorization

Formal Metadata

Title
Rank optimality for the Burer-Monteiro factorization
Title of Series
Author
License
CC Attribution - NonCommercial - NoDerivatives 2.0 Generic:
You are free to use, copy, distribute and transmit the work or content in unchanged form for any legal and non-commercial purpose as long as the work is attributed to the author in the manner specified by the author or licensor.
Identifiers
Publisher
Release Date
2020
Language
English

Content Metadata

Subject Area
Abstract
The Burer-Monteiro factorization is a classical heuristic used to speed up the solving of large scale semidefinite programs when the solution is expected to be low rank: One writes the solution as the product of thinner matrices, and optimizes over the (low-dimensional) factors instead of over the full matrix. Even though the factorized problem is non-convex, one observes that standard first-order algorithms can often solve it to global optimality. This has been rigorously proved by Boumal, Voroninski and Bandeira, but only under the assumption that the factorization rank is large enough, larger than what numerical experiments suggest. We will describe this result, and investigate its optimality. More specifically, we will show that, up to a minor improvement, it is optimal: without additional hypotheses on the semidefinite problem at hand, first-order algorithms can fail if the factorization rank is smaller than predicted by current theory.
Keywords nonconvex optimization phase retrieval low-rank matrix recovery
Feedback