Via Zoom: Polynomial Time Guarantees for the Burer-Monteiro Method

Friday, March 27, 2020 - 1:00pm to 2:00pm

Event Calendar Category

Other LIDS Events

Speaker Name

Diego Cifuentes

Affiliation

MIT Math

Abstract

The Burer-Monteiro method is one of the most widely used techniques for solving large-scale semidefinite programs (SDP). The basic idea is to solve a nonconvex program in Y, where Y is an n×p matrix such that X = YYT. In this paper, we show that this method can solve SDPs in polynomial time in a smoothed analysis setting. More precisely, we consider an SDP whose domain satisfies some compactness and smoothness assumptions and slightly perturb the cost matrix and the constraints. We show that if p ≳ √(2+2η)m, where m is the number of constraints and η>0 is any fixed constant, then the Burer-Monteiro method can solve SDPs to any desired accuracy in polynomial time, in the setting of smooth analysis. Our bound on p approaches the celebrated Barvinok-Pataki bound in the limit as η goes to zero, beneath which it is known that the nonconvex program can be suboptimal.

Join Zoom Meeting:  https://mit.zoom.us/j/790392024

Meeting ID: 790 392 024