[{"main_file_link":[{"url":"https://doi.org/10.1145/3832046.3832063","open_access":"1"}],"OA_type":"free access","author":[{"id":"3D50B0BA-F248-11E8-B48F-1D18A9856A87","last_name":"Kolmogorov","full_name":"Kolmogorov, Vladimir","first_name":"Vladimir"},{"full_name":"Naldi, Simone","last_name":"Naldi","first_name":"Simone"},{"first_name":"Jeferson","full_name":"Zapata, Jeferson","id":"00223538-AF8F-11E9-A4C7-F729E6697425","last_name":"Zapata"}],"date_created":"2026-08-30T22:01:44Z","OA_place":"publisher","article_type":"original","publication_identifier":{"issn":["1932-2232"],"eissn":["1932-2240"]},"abstract":[{"lang":"eng","text":"We consider the problem of certifying the feasibility of a (possibly degenerate) semidefinite programming problem represented by rational input data together with a numerical solution that is guaranteed to be sufficiently close to an exact solution of maximal rank. Our method constructs a polynomial system whose set of real solutions has an isolated point that satisfies the input program. An experimental comparison between the corresponding symbolic-numerical algorithm and the purely symbolic algorithm from [3, 5] shows that the hybrid algorithm is able to certify instances where the exact method fails."}],"fulldoi":"https://doi.org/10.1145/3832046.3832063","acknowledgement":"This extended abstract is based on the paper [7], accepted for publication at SIAM\r\nJ. Opt. on April 22, 2025, to which we refer for technical details and complete proofs. This work has been\r\nsupported by the Doctoral Programme Vienna Graduate School on Computational Optimization (VGSCO)\r\nwhich was funded by FWF (Austrian Science Fund), project W 1260-N35, and partially supported by the\r\nANR JCJC project ANR-21-CE48-0006-01 “HYPERSPACE”.\r\n","scopus_import":"1","date_published":"2025-12-01T00:00:00Z","_id":"22774","corr_author":"1","date_updated":"2026-09-09T08:17:05Z","volume":59,"status":"public","title":"Certifying solutions of degenerate semidefinite programs","oa":1,"page":"147-152","project":[{"grant_number":"W1260-N35","_id":"9B9290DE-BA93-11EA-9121-9846C619BF3A","name":"Vienna Graduate School on Computational Optimization"}],"month":"12","external_id":{"unknown":["2405.13625"]},"intvolume":"        59","oa_version":"Published Version","day":"01","type":"journal_article","issue":"4","year":"2025","department":[{"_id":"VlKo"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication_status":"published","language":[{"iso":"eng"}],"publisher":"ACM","doi":"10.1145/3832046.3832063","citation":{"mla":"Kolmogorov, Vladimir, et al. “Certifying Solutions of Degenerate Semidefinite Programs.” <i>ACM Communications in Computer Algebra</i>, vol. 59, no. 4, ACM, 2025, pp. 147–52, doi:<a href=\"https://doi.org/10.1145/3832046.3832063\">10.1145/3832046.3832063</a>.","ama":"Kolmogorov V, Naldi S, Zapata J. Certifying solutions of degenerate semidefinite programs. <i>ACM Communications in Computer Algebra</i>. 2025;59(4):147-152. doi:<a href=\"https://doi.org/10.1145/3832046.3832063\">10.1145/3832046.3832063</a>","ieee":"V. Kolmogorov, S. Naldi, and J. Zapata, “Certifying solutions of degenerate semidefinite programs,” <i>ACM Communications in Computer Algebra</i>, vol. 59, no. 4. ACM, pp. 147–152, 2025.","short":"V. Kolmogorov, S. Naldi, J. Zapata, ACM Communications in Computer Algebra 59 (2025) 147–152.","apa":"Kolmogorov, V., Naldi, S., &#38; Zapata, J. (2025). Certifying solutions of degenerate semidefinite programs. <i>ACM Communications in Computer Algebra</i>. ACM. <a href=\"https://doi.org/10.1145/3832046.3832063\">https://doi.org/10.1145/3832046.3832063</a>","chicago":"Kolmogorov, Vladimir, Simone Naldi, and Jeferson Zapata. “Certifying Solutions of Degenerate Semidefinite Programs.” <i>ACM Communications in Computer Algebra</i>. ACM, 2025. <a href=\"https://doi.org/10.1145/3832046.3832063\">https://doi.org/10.1145/3832046.3832063</a>.","ista":"Kolmogorov V, Naldi S, Zapata J. 2025. Certifying solutions of degenerate semidefinite programs. ACM Communications in Computer Algebra. 59(4), 147–152."},"publication":"ACM Communications in Computer Algebra","article_processing_charge":"No"}]