An Adaptive Augmented Lagrangian Method for Deterministic and Stochastic Nonconvex Optimization

[2608.27676] An Adaptive Augmented Lagrangian Method for Deterministic and Stochastic Nonconvex Optimization Skip to main content Search Submit Donate Log in Mathematics > Optimization and Control arXiv:2608.27676 (math) [Submitted on 27 Aug 2026] Title: An Adaptive Augmented Lagrangian Method for Deterministic and Stochastic Nonconvex Optimization Authors: Tianzhu Liu , Michael J. O'Neill View PDF HTML (experimental) Abstract: We present an inexact Augmented Lagrangian algorithm for solving nonlinear, non-convex optimization problems. Unlike most recently proposed Augmented Lagrangian methods with worst-case complexity guarantees, we utilize adaptive penalty parameter updates and full dual stepsizes. We show that the method matches the best known worst-case complexity results for Augmented Lagrangian methods (up to logarithmic factors) when both the function and constraints are deterministic, when the function is stochastic and the constraints are deterministic, and when both are stochastic. Experiments on CUTEst test problems confirm the practical advantages of the proposed approach over Augmented Lagrangian methods with non-adaptive penalty parameters and/or short dual step sizes in the deterministic setting. Numerical results on stochastic constrained optimization problems in machine learning also confirm these findings. Subjects: Optimization and Control (math.OC) MSC classes: 49M37, 65K05, 65K10, 90C15, 90C30, 90C55 Cite as: arXiv:2608.27676 [math.OC] (or arXiv:2608.27676v1 [math.OC] for this version) https://doi.org/10.48550/arXiv.2608.27676 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Michael O'Neill [ view email ] [v1] Thu, 27 Aug 2026 20:06:05 UTC (17,181 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: math.OC < prev | next > new | recent | 2026-08 Change to browse by: math References & Citations SciX Google Scholar Semantic Scholar export BibTeX citation 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)

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