{"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/disciplined-multi-convex-programming","title":"Disciplined Multi-Convex Programming","arxiv_id":"1609.03285","date":"2016-09-12","proceeding":null,"authors":["Xinyue Shen","Steven Diamond","Madeleine Udell","Yuantao Gu","Stephen Boyd"],"abstract":"A multi-convex optimization problem is one in which the variables can be partitioned into sets over which the problem is convex when the other variables are fixed. Multi-convex problems are generally solved approximately using variations on alternating or cyclic minimization. Multi-convex problems arise in many applications, such as nonnegative matrix factorization, generalized low rank models, and structured control synthesis, to name just a few. In most applications to date the multi-convexity is simple to verify by hand. In this paper we study the automatic detection and verification of multi-convexity using the ideas of disciplined convex programming. We describe an implementation of our proposed method that detects and verifies multi-convexity, and then invokes one of the general solution methods.","url_abs":"https://arxiv.org/abs/1609.03285v2","url_pdf":"https://arxiv.org/pdf/1609.03285v2.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":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"disciplined-multi-convex-programming","repo_url":"https://github.com/madeleineudell/MultiConvex.jl","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"disciplined-multi-convex-programming","repo_url":"https://github.com/cvxgrp/dmcp","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null},{"paper_slug":"disciplined-multi-convex-programming","repo_url":"https://github.com/fernando-duarte/MultiConvex.jl","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1609.03285","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}