Akian, Marianne; Allamigeon, Xavier; Gaubert, Stéphane; Sergeev, Sergei Signed tropicalization of polar cones. arXiv:2305.05637 Preprint, arXiv:2305.05637 [math.OC] (2023). MSC: 15A80 49N15 90C24 14T90 BibTeX Cite \textit{M. Akian} et al., ``Signed tropicalization of polar cones'', Preprint, arXiv:2305.05637 [math.OC] (2023) Full Text: arXiv OA License
Allamigeon, Xavier; Boyet, Marin; Gaubert, Stéphane Piecewise affine dynamical models of Petri nets – application to emergency call centers. (English) Zbl 1522.68356 Fundam. Inform. 183, No. 3-4, 169-201 (2021). MSC: 68Q85 14T90 90C40 90C90 PDFBibTeX XMLCite \textit{X. Allamigeon} et al., Fundam. Inform. 183, No. 3--4, 169--201 (2021; Zbl 1522.68356) Full Text: DOI arXiv
Allamigeon, Xavier; Benchimol, Pascal; Gaubert, Stéphane; Joswig, Michael What tropical geometry tells us about the complexity of linear programming. (English) Zbl 1459.90124 SIAM Rev. 63, No. 1, 123-164 (2021). MSC: 90C05 90C51 90C24 14T10 PDFBibTeX XMLCite \textit{X. Allamigeon} et al., SIAM Rev. 63, No. 1, 123--164 (2021; Zbl 1459.90124) Full Text: DOI
Allamigeon, Xavier; Gaubert, Stéphane; Skomra, Mateusz Tropical spectrahedra. (English) Zbl 1437.14066 Discrete Comput. Geom. 63, No. 3, 507-548 (2020). MSC: 14T10 14T15 90C22 14P10 12J25 15A03 15A15 16Y60 52A37 14T25 PDFBibTeX XMLCite \textit{X. Allamigeon} et al., Discrete Comput. Geom. 63, No. 3, 507--548 (2020; Zbl 1437.14066) Full Text: DOI arXiv
Allamigeon, Xavier; Aznag, Abdellah; Gaubert, Stéphane; Hamdi, Yassine The tropicalization of the entropic barrier. arXiv:2010.10205 Preprint, arXiv:2010.10205 [math.OC] (2020). MSC: 90C51 14T05 BibTeX Cite \textit{X. Allamigeon} et al., ``The tropicalization of the entropic barrier'', Preprint, arXiv:2010.10205 [math.OC] (2020) Full Text: arXiv OA License
Allamigeon, Xavier; Gaubert, Stéphane; Skomra, Mateusz The tropical analogue of the Helton-Nie conjecture is true. (English) Zbl 1471.14127 J. Symb. Comput. 91, 129-148 (2019). Reviewer: Alperen Ali Ergur (Pittsburgh) MSC: 14T15 14T20 90C22 14P10 68W30 PDFBibTeX XMLCite \textit{X. Allamigeon} et al., J. Symb. Comput. 91, 129--148 (2019; Zbl 1471.14127) Full Text: DOI arXiv
Allamigeon, Xavier; Benchimol, Pascal; Gaubert, Stéphane; Joswig, Michael Log-barrier interior point methods are not strongly polynomial. (English) Zbl 1391.90637 SIAM J. Appl. Algebra Geom. 2, No. 1, 140-178 (2018). MSC: 90C51 14T05 PDFBibTeX XMLCite \textit{X. Allamigeon} et al., SIAM J. Appl. Algebra Geom. 2, No. 1, 140--178 (2018; Zbl 1391.90637) Full Text: DOI arXiv
Allamigeon, Xavier; Katz, Ricardo D. Tropicalization of facets of polytopes. (English) Zbl 1398.14063 Linear Algebra Appl. 523, 79-101 (2017). MSC: 14T05 52A30 52B05 52B12 PDFBibTeX XMLCite \textit{X. Allamigeon} and \textit{R. D. Katz}, Linear Algebra Appl. 523, 79--101 (2017; Zbl 1398.14063) Full Text: DOI arXiv Link
Allamigeon, Xavier; Benchimol, Pascal; Gaubert, Stéphane; Joswig, Michael Tropicalizing the simplex algorithm. (English) Zbl 1334.14033 SIAM J. Discrete Math. 29, No. 2, 751-795 (2015). Reviewer: Péter E. Frenkel (Budapest) MSC: 14T05 90C05 PDFBibTeX XMLCite \textit{X. Allamigeon} et al., SIAM J. Discrete Math. 29, No. 2, 751--795 (2015; Zbl 1334.14033) Full Text: DOI arXiv
Allamigeon, Xavier; Benchimol, Pascal; Gaubert, Stéphane; Joswig, Michael Combinatorial simplex algorithms can solve mean payoff games. (English) Zbl 1336.90057 SIAM J. Optim. 24, No. 4, 2096-2117 (2014). Reviewer: Maxim Ivanov Todorov (San Andres Cholula) MSC: 90C05 91A07 14T05 03C98 PDFBibTeX XMLCite \textit{X. Allamigeon} et al., SIAM J. Optim. 24, No. 4, 2096--2117 (2014; Zbl 1336.90057) Full Text: DOI arXiv
Allamigeon, Xavier; Benchimol, Pascal; Gaubert, Stéphane The tropical shadow-vertex algorithm solves mean payoff games in polynomial time on average. (English) Zbl 1409.68129 Esparza, Javier (ed.) et al., Automata, languages, and programming. 41st international colloquium, ICALP 2014, Copenhagen, Denmark, July 8–11, 2014. Proceedings, Part I. Berlin: Springer. Lect. Notes Comput. Sci. 8572, 89-100 (2014). MSC: 68Q25 14T05 16Y60 52B20 91A43 PDFBibTeX XMLCite \textit{X. Allamigeon} et al., Lect. Notes Comput. Sci. 8572, 89--100 (2014; Zbl 1409.68129) Full Text: DOI arXiv
Allamigeon, Xavier; Benchimol, Pascal; Gaubert, Stéphane; Joswig, Michael Long and winding central paths. arXiv:1405.4161 Preprint, arXiv:1405.4161 [math.OC] (2014). MSC: 90C51 14T05 BibTeX Cite \textit{X. Allamigeon} et al., ``Long and winding central paths'', Preprint, arXiv:1405.4161 [math.OC] (2014) Full Text: arXiv OA License
Allamigeon, Xavier; Katz, Ricardo D. Minimal external representations of tropical polyhedra. (English) Zbl 1312.52002 J. Comb. Theory, Ser. A 120, No. 4, 907-940 (2013). MSC: 52A01 14T05 52B20 PDFBibTeX XMLCite \textit{X. Allamigeon} and \textit{R. D. Katz}, J. Comb. Theory, Ser. A 120, No. 4, 907--940 (2013; Zbl 1312.52002) Full Text: DOI arXiv
Allamigeon, Xavier; Gaubert, Stéphane; Goubault, Éric Computing the vertices of tropical polyhedra using directed hypergraphs. (English) Zbl 1312.52001 Discrete Comput. Geom. 49, No. 2, 247-279 (2013). MSC: 52A01 05C65 14T05 52B05 68Q17 68U05 PDFBibTeX XMLCite \textit{X. Allamigeon} et al., Discrete Comput. Geom. 49, No. 2, 247--279 (2013; Zbl 1312.52001) Full Text: DOI arXiv
Allamigeon, Xavier; Gaubert, Stéphane; Katz, Ricardo D. Tropical polar cones, hypergraph transversals, and mean payoff games. (English) Zbl 1217.14047 Linear Algebra Appl. 435, No. 7, 1549-1574 (2011). MSC: 14T05 15A80 52A01 16Y60 PDFBibTeX XMLCite \textit{X. Allamigeon} et al., Linear Algebra Appl. 435, No. 7, 1549--1574 (2011; Zbl 1217.14047) Full Text: DOI arXiv
Allamigeon, Xavier; Gaubert, Stéphane; Katz, Ricardo D. The number of extreme points of tropical polyhedra. (English) Zbl 1246.14078 J. Comb. Theory, Ser. A 118, No. 1, 162-189 (2011). Reviewer: Serge Lawrencenko (Moskva) MSC: 14T05 52A01 52B05 PDFBibTeX XMLCite \textit{X. Allamigeon} et al., J. Comb. Theory, Ser. A 118, No. 1, 162--189 (2011; Zbl 1246.14078) Full Text: DOI arXiv
Allamigeon, Xavier; Gaubert, Stéphane; Goubault, Éric The tropical double description method. (English) Zbl 1230.52024 Marion, Jean-Yves (ed.) et al., STACS 2010. 27th international symposium on theoretical aspects of computer science, Nancy, France, March 4–6, 2010. Wadern: Schloss Dagstuhl – Leibniz Zentrum für Informatik (ISBN 978-3-939897-16-3). LIPIcs – Leibniz International Proceedings in Informatics 5, 47-58, electronic only (2010). MSC: 52B10 14T05 52B55 52A01 15A80 PDFBibTeX XMLCite \textit{X. Allamigeon} et al., LIPIcs -- Leibniz Int. Proc. Inform. 5, 47--58 (2010; Zbl 1230.52024) Full Text: DOI Link