Time-Varying Semidefinite Programming: Path Following a Burer-Monteiro Factorization
Abstract
We present an online algorithm for time-varying semidefinite programs (TV-SDPs), based on the tracking of the solution trajectory of a low-rank matrix factorization, also known as the Burer-Monteiro factorization, in a path-following procedure. There, a predictor-corrector algorithm solves a sequence of linearized systems. This requires the introduction of a horizontal space constraint to ensure the local injectivity of the low-rank factorization. The method produces a sequence of approximate solutions for the original TV-SDP problem, for which we show that they stay close to the optimal solution path if properly initialized. Numerical experiments for a time-varying max-cut SDP relaxation demonstrate the computational advantages of the proposed method for tracking TV-SDPs in terms of runtime compared to off-the-shelf interior point methods.
Cite
@article{arxiv.2210.08387,
title = {Time-Varying Semidefinite Programming: Path Following a Burer-Monteiro Factorization},
author = {Antonio Bellon and Mareike Dressler and Vyacheslav Kungurtsev and Jakub Marecek and André Uschmajew},
journal= {arXiv preprint arXiv:2210.08387},
year = {2024}
}
Comments
24 pages, 3 figures