The Golden Ratio Proximal ADMM with Norm Independent Step-Sizes for Separable Convex Optimization

Mathematics > Optimization and Control [Submitted on 7 Oct 2025 (v1), last revised 16 Jun 2026 (this version, v3)] Title:The Golden Ratio Proximal ADMM with Norm Independent Step-Sizes for Separable Convex Optimization View PDF HTML (experimental)Abstract:In this work, we propose two step-size strategies for the Golden ratio proximal ADMM (GrpADMM) to solve linearly constrained separable convex optimization problems. Both strategies eliminate explicit operator norm estimates by relying on inexpensive local information computed at the current iterate and requiring no backtracking. However, the key difference is that the second step-size strategy allows recovery from poor initial steps and can increase from iteration to iteration. Under standard assumptions, we establish global convergence of the generated iterates and derive sublinear convergence rates for both algorithms. We also obtain pointwise convergence rate results for the iterates of the algorithms. In addition, we show that the first proposed step-size rule for GrpADMM reduces to the fixed-step-size counterpart when the initial step-size is chosen below a certain threshold. Preliminary numerical experiments demonstrate the practical adaptability and effectiveness of the proposed approaches. Submission history From: Santanu Soe [view email][v1] Tue, 7 Oct 2025 10:48:53 UTC (1,394 KB) [v2] Thu, 16 Apr 2026 16:59:15 UTC (4,168 KB) [v3] Tue, 16 Jun 2026 03:39:20 UTC (4,169 KB) References & Citations Loading... 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?) ScienceCast (What is ScienceCast?) Demos 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.