{"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-fast-semidefinite-approach-to-solving","title":"A Fast Semidefinite Approach to Solving Binary Quadratic Problems","arxiv_id":"1304.0840","date":"2013-04-03","proceeding":"CVPR 2013 6","authors":["Peng Wang","Chunhua Shen","Anton Van Den Hengel"],"abstract":"Many computer vision problems can be formulated as binary quadratic programs\n(BQPs). Two classic relaxation methods are widely used for solving BQPs,\nnamely, spectral methods and semidefinite programming (SDP), each with their\nown advantages and disadvantages. Spectral relaxation is simple and easy to\nimplement, but its bound is loose. Semidefinite relaxation has a tighter bound,\nbut its computational complexity is high for large scale problems. We present a\nnew SDP formulation for BQPs, with two desirable properties. First, it has a\nsimilar relaxation bound to conventional SDP formulations. Second, compared\nwith conventional SDP methods, the new SDP formulation leads to a significantly\nmore efficient and scalable dual optimization approach, which has the same\ndegree of complexity as spectral methods. Extensive experiments on various\napplications including clustering, image segmentation, co-segmentation and\nregistration demonstrate the usefulness of our SDP formulation for solving\nlarge-scale BQPs.","url_abs":"http://arxiv.org/abs/1304.0840v1","url_pdf":"http://arxiv.org/pdf/1304.0840v1.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-fast-semidefinite-approach-to-solving","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":"clustering","task_name":"Clustering"},{"task_slug":"image-segmentation","task_name":"Image Segmentation"},{"task_slug":"segmentation","task_name":"Segmentation"},{"task_slug":"semantic-segmentation","task_name":"Semantic Segmentation"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}