{"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/a-projection-method-for-metric-constrained","title":"A Projection Method for Metric-Constrained Optimization","arxiv_id":"1806.01678","date":"2018-06-05","proceeding":null,"authors":["Nate Veldt","David Gleich","Anthony Wirth","James Saunderson"],"abstract":"We outline a new approach for solving optimization problems which enforce\ntriangle inequalities on output variables. We refer to this as\nmetric-constrained optimization, and give several examples where problems of\nthis form arise in machine learning applications and theoretical approximation\nalgorithms for graph clustering. Although these problem are interesting from a\ntheoretical perspective, they are challenging to solve in practice due to the\nhigh memory requirement of black-box solvers. In order to address this\nchallenge we first prove that the metric-constrained linear program relaxation\nof correlation clustering is equivalent to a special case of the metric\nnearness problem. We then developed a general solver for metric-constrained\nlinear and quadratic programs by generalizing and improving a simple projection\nalgorithm originally developed for metric nearness. We give several novel\napproximation guarantees for using our framework to find lower bounds for\noptimal solutions to several challenging graph clustering problems. We also\ndemonstrate the power of our framework by solving optimizing problems involving\nup to 10^{8} variables and 10^{11} constraints.","url_abs":"http://arxiv.org/abs/1806.01678v1","url_pdf":"http://arxiv.org/pdf/1806.01678v1.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":"a-projection-method-for-metric-constrained","repo_url":"https://github.com/nveldt/MetricOptimization","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"clustering","task_name":"Clustering"},{"task_slug":"graph-clustering","task_name":"Graph Clustering"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/1806.01678","atlas_url":"https://app.syntology.ai/?focus=1806.01678","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}