{"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/the-mixing-method-low-rank-coordinate-descent","title":"The Mixing method: low-rank coordinate descent for semidefinite programming with diagonal constraints","arxiv_id":"1706.00476","date":"2017-06-01","proceeding":null,"authors":["Po-Wei Wang","Wei-Cheng Chang","J. Zico Kolter"],"abstract":"In this paper, we propose a low-rank coordinate descent approach to\nstructured semidefinite programming with diagonal constraints. The approach,\nwhich we call the Mixing method, is extremely simple to implement, has no free\nparameters, and typically attains an order of magnitude or better improvement\nin optimization performance over the current state of the art. We show that the\nmethod is strictly decreasing, converges to a critical point, and further that\nfor sufficient rank all non-optimal critical points are unstable. Moreover, we\nprove that with a step size, the Mixing method converges to the global optimum\nof the semidefinite program almost surely in a locally linear rate under random\ninitialization. This is the first low-rank semidefinite programming method that\nhas been shown to achieve a global optimum on the spherical manifold without\nassumption. We apply our algorithm to two related domains: solving the maximum\ncut semidefinite relaxation, and solving a maximum satisfiability relaxation\n(we also briefly consider additional applications such as learning word\nembeddings). In all settings, we demonstrate substantial improvement over the\nexisting state of the art along various dimensions, and in total, this work\nexpands the scope and scale of problems that can be solved using semidefinite\nprogramming methods.","url_abs":"http://arxiv.org/abs/1706.00476v3","url_pdf":"http://arxiv.org/pdf/1706.00476v3.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":"the-mixing-method-low-rank-coordinate-descent","repo_url":"https://github.com/locuslab/mixing","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":{"status":"unanswered"}}],"tasks":[{"task_slug":"learning-word-embeddings","task_name":"Learning Word Embeddings"},{"task_slug":"word-embeddings","task_name":"Word Embeddings"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1706.00476","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}