{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/optimization-of-graph-total-variation-via","title":"Optimization of Graph Total Variation via Active-Set-based Combinatorial Reconditioning","arxiv_id":"2002.12236","date":"2020-02-27","proceeding":null,"authors":["Zhenzhang Ye","Thomas Möllenhoff","Tao Wu","Daniel Cremers"],"abstract":"Structured convex optimization on weighted graphs finds numerous applications in machine learning and computer vision. In this work, we propose a novel adaptive preconditioning strategy for proximal algorithms on this problem class. Our preconditioner is driven by a sharp analysis of the local linear convergence rate depending on the \"active set\" at the current iterate. We show that nested-forest decomposition of the inactive edges yields a guaranteed local linear convergence rate. Further, we propose a practical greedy heuristic which realizes such nested decompositions and show in several numerical experiments that our reconditioning strategy, when applied to proximal gradient or primal-dual hybrid gradient algorithm, achieves competitive performances. Our results suggest that local convergence analysis can serve as a guideline for selecting variable metrics in proximal algorithms.","url_abs":"https://arxiv.org/abs/2002.12236v1","url_pdf":"https://arxiv.org/pdf/2002.12236v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"optimization-of-graph-total-variation-via","repo_url":"https://github.com/zhenzhangye/graph_TV_recond","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/2002.12236","atlas_url":"https://app.syntology.ai/?focus=2002.12236","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}