Towards faster first order methods: A continuous-time model to interpolate between speed and function value restart

[2506.11267] Towards faster first order methods: A continuous-time model to interpolate between speed and function value restart Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Optimization and Control arXiv:2506.11267 (math) [Submitted on 12 Jun 2025 ( v1 ), last revised 10 Apr 2026 (this version, v3)] Title: Towards faster first order methods: A continuous-time model to interpolate between speed and function value restart Authors: Juan José Maulén , Huiyuan Guo , Juan Peypouquet View a PDF of the paper titled Towards faster first order methods: A continuous-time model to interpolate between speed and function value restart, by Juan Jos\'e Maul\'en and 2 other authors View PDF HTML (experimental) Abstract: We introduce a new restarting scheme for a continuous inertial dynamics with Hessian driven-damping, and establish a linear convergence rate for the function values along the restarted trajectories. The proposed routine is implemented without knowing the strong convexity parameter, and is a generalization of existing speed restart schemes. It interpolates between speed and function value restarts, considerably delaying the restarting time, while preserving convergence and function value decrease. Numerical experiments show an improvement in the convergence rates for both continuous-time dynamical systems, and the associated accelerated first-order algorithms derived via time discretization. Subjects: Optimization and Control (math.OC) Cite as: arXiv:2506.11267 [math.OC] (or arXiv:2506.11267v3 [math.OC] for this version) https://doi.org/10.48550/arXiv.2506.11267 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Juan Jose Maulen Muñoz [ view email ] [v1] Thu, 12 Jun 2025 20:19:24 UTC (201 KB) [v2] Thu, 2 Apr 2026 23:40:12 UTC (1,067 KB) [v3] Fri, 10 Apr 2026 04:57:57 UTC (1,067 KB) Full-text links: Access Paper: View a PDF of the paper titled Towards faster first order methods: A continuous-time model to interpolate between speed and function value restart, by Juan Jos\'e Maul\'en and 2 other authors View PDF HTML (experimental) TeX Source view license Current browse context: math.OC < prev | next > new | recent | 2025-06 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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