[go: up one dir, main page]
More Web Proxy on the site http://driver.im/
Skip to main content
We gratefully acknowledge support from the Simons Foundation, member institutions, and all contributors. Donate
arXiv logo
Cornell University Logo

Mathematics > Optimization and Control

arXiv:2210.08387 (math)
[Submitted on 15 Oct 2022 (v1), last revised 9 Jan 2024 (this version, v3)]

Title:Time-Varying Semidefinite Programming: Path Following a Burer-Monteiro Factorization

Authors:Antonio Bellon, Mareike Dressler, Vyacheslav Kungurtsev, Jakub Marecek, André Uschmajew
View PDF HTML (experimental)
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.
Comments: 24 pages, 3 figures
Subjects: Optimization and Control (math.OC); Numerical Analysis (math.NA)
MSC classes: primary: 90C22, 90C30, 90C31, secondary: 49M15
Cite as: arXiv:2210.08387 [math.OC]
  (or arXiv:2210.08387v3 [math.OC] for this version)
  https://doi.org/10.48550/arXiv.2210.08387
Journal reference: SIAM Journal on Optimization, 2024
Related DOI: https://doi.org/10.1137/22M1529762

Submission history

From: Antonio Bellon [view email]
[v1] Sat, 15 Oct 2022 22:29:44 UTC (1,137 KB)
[v2] Tue, 5 Dec 2023 17:23:56 UTC (313 KB)
[v3] Tue, 9 Jan 2024 12:31:15 UTC (313 KB)
Full-text links:

Access Paper:

view license
Current browse context:
math.OC
< prev   |   next >
new | recent | 2022-10
Change to browse by:
cs
cs.NA
math
math.NA

References & Citations

export BibTeX citation

Bookmark

BibSonomy logo Reddit logo

Bibliographic and Citation Tools

Bibliographic Explorer (What is the Explorer?)
Connected Papers (What is Connected Papers?)
Litmaps (What is Litmaps?)
scite Smart Citations (What are Smart Citations?)

Code, Data and Media Associated with this Article

alphaXiv (What is alphaXiv?)
CatalyzeX Code Finder for Papers (What is CatalyzeX?)
DagsHub (What is DagsHub?)
Gotit.pub (What is GotitPub?)
Hugging Face (What is Huggingface?)
Papers with Code (What is Papers with Code?)
ScienceCast (What is ScienceCast?)

Demos

Replicate (What is Replicate?)
Hugging Face Spaces (What is Spaces?)
TXYZ.AI (What is TXYZ.AI?)

Recommenders and Search Tools

Influence Flower (What are Influence Flowers?)
CORE Recommender (What is CORE?)

arXivLabs: experimental projects with community collaborators

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.

Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)