A Massively Parallel Interior-Point Method for Arrowhead Linear Programs with Local Linking Structure

[2412.07731] A Massively Parallel Interior-Point Method for Arrowhead Linear Programs with Local Linking Structure Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Optimization and Control arXiv:2412.07731 (math) [Submitted on 10 Dec 2024 ( v1 ), last revised 9 Apr 2026 (this version, v2)] Title: A Massively Parallel Interior-Point Method for Arrowhead Linear Programs with Local Linking Structure Authors: Nils-Christian Kempke , Daniel Rehfeldt , Thorsten Koch View a PDF of the paper titled A Massively Parallel Interior-Point Method for Arrowhead Linear Programs with Local Linking Structure, by Nils-Christian Kempke and 2 other authors View PDF HTML (experimental) Abstract: In practice, non-specialized interior point algorithms often cannot utilize the massively parallel compute resources offered by modern many- and multi-core compute platforms. However, efficient distributed solution techniques are required, especially for large-scale linear programs. This article describes a new decomposition technique for systems of linear equations implemented in the parallel interior-point solver PIPS-IPM++. The algorithm exploits a matrix structure commonly found in optimization problems: a doubly-bordered block-diagonal or arrowhead structure. This structure is preserved in the linear KKT systems solved during each iteration of the interior-point method. We present a hierarchical Schur complement decomposition that distributes and solves the linear optimization problem; it is designed for high-performance architectures and scales well with the availability of additional computing resources. The decomposition approach uses the border constraints' locality to decouple the factorization process. Our approach is motivated by large-scale unit commitment problems. We demonstrate the performance of our method on a set of mid-to large-scale instances, some of which have more than 10^9 nonzeros in their constraint matrix. Subjects: Optimization and Control (math.OC) MSC classes: 90C05, 90C51 (Primary), 65F05, 65K05, 65Y05, 90C06, 90-08 (Secondary) Report number: ZIB-Report 24-13 Cite as: arXiv:2412.07731 [math.OC] (or arXiv:2412.07731v2 [math.OC] for this version) https://doi.org/10.48550/arXiv.2412.07731 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Nils-Christian Kempke [ view email ] [v1] Tue, 10 Dec 2024 18:27:09 UTC (168 KB) [v2] Thu, 9 Apr 2026 08:16:15 UTC (120 KB) Full-text links: Access Paper: View a PDF of the paper titled A Massively Parallel Interior-Point Method for Arrowhead Linear Programs with Local Linking Structure, by Nils-Christian Kempke and 2 other authors View PDF HTML (experimental) TeX Source view license Current browse context: math.OC < prev | next > new | recent | 2024-12 Change to browse by: math References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs 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? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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