{"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/biconvex-relaxation-for-semidefinite","title":"Biconvex Relaxation for Semidefinite Programming in Computer Vision","arxiv_id":"1605.09527","date":"2016-05-31","proceeding":null,"authors":["Sohil Shah","Abhay Kumar","Carlos Castillo","David Jacobs","Christoph Studer","Tom Goldstein"],"abstract":"Semidefinite programming is an indispensable tool in computer vision, but\ngeneral-purpose solvers for semidefinite programs are often too slow and memory\nintensive for large-scale problems. We propose a general framework to\napproximately solve large-scale semidefinite problems (SDPs) at low complexity.\nOur approach, referred to as biconvex relaxation (BCR), transforms a general\nSDP into a specific biconvex optimization problem, which can then be solved in\nthe original, low-dimensional variable space at low complexity. The resulting\nbiconvex problem is solved using an efficient alternating minimization (AM)\nprocedure. Since AM has the potential to get stuck in local minima, we propose\na general initialization scheme that enables BCR to start close to a global\noptimum - this is key for our algorithm to quickly converge to optimal or\nnear-optimal solutions. We showcase the efficacy of our approach on three\napplications in computer vision, namely segmentation, co-segmentation, and\nmanifold metric learning. BCR achieves solution quality comparable to\nstate-of-the-art SDP methods with speedups between 4X and 35X. At the same\ntime, BCR handles a more general set of SDPs than previous approaches, which\nare more specialized.","url_abs":"http://arxiv.org/abs/1605.09527v2","url_pdf":"http://arxiv.org/pdf/1605.09527v2.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":"biconvex-relaxation-for-semidefinite","repo_url":"https://github.com/Axeldnahcram/biconvex_relaxation","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"metric-learning","task_name":"Metric Learning"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}