article published Vladimir Kolmogorov author 3D50B0BA-F248-11E8-B48F-1D18A9856A87 Simone Naldi author Jeferson Zapata author 00223538-AF8F-11E9-A4C7-F729E6697425 VlKo department Vienna Graduate School on Computational Optimization project 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. ACM2025 eng 1932-2232 1932-224010.1145/3832046.3832063 594147-152 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>. 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. 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> V. Kolmogorov, S. Naldi, J. Zapata, ACM Communications in Computer Algebra 59 (2025) 147–152. 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> Kolmogorov V, Naldi S, Zapata J. 2025. Certifying solutions of degenerate semidefinite programs. ACM Communications in Computer Algebra. 59(4), 147–152. 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>. 227742026-08-30T22:01:44Z2026-09-09T08:17:05Z