Bibliography

Major publications by the team in recent years

• 1M. Akian.
  Densities of idempotent measures and large deviations, in: Transactions of the American Mathematical Society, 1999, vol. 351, n^o 11, pp. 4515–4543.
• 2M. Akian, R. Bapat, S. Gaubert.
  Max-plus algebras, in: Handbook of Linear Algebra (Discrete Mathematics and Its Applications), L. Hogben (editor), Chapman & Hall/CRC, 2006, vol. 39, Chapter 25.
• 3M. Akian, S. Gaubert.
  Spectral Theorem for Convex Monotone Homogeneous Maps, and ergodic Control, in: Nonlinear Analysis. Theory, Methods & Applications, 2003, vol. 52, n^o 2, pp. 637-679.
  http://hal.inria.fr/inria-00000201/en/
• 4M. Akian, S. Gaubert, B. Lemmens, R. Nussbaum.
  Iteration of order preserving subhomogeneous maps on a cone, in: Math. Proc. Cambridge Philos. Soc., 2006, vol. 140, n^o 1, pp. 157–176.
  http://www.arxiv.org/abs/math.DS/0410084
• 5M. Akian, A. Sulem, M. Taksar.
  Dynamic optimisation of long term growth rate for a portfolio with transaction costs and logarithmic utility, in: Mathematical Finance, 2001, vol. 11, n^o 2, pp. 153–188.
• 6F. Baccelli, G. Cohen, G. Olsder, J.-P. Quadrat.
  Synchronisation and Linearity, Wiley, 1992.
• 7J. Cochet-Terrasson, S. Gaubert, J. Gunawardena.
  A constructive fixed point theorem for min-max functions, in: Dynamics and Stability of Systems, 1999, vol. 14, n^o 4.
• 8G. Cohen, S. Gaubert, J.-P. Quadrat.
  Duality and Separation Theorems in Idempotent Semimodules, in: Linear Algebra and Appl., 2004, vol. 379, pp. 395–422.
  http://arxiv.org/abs/math.FA/0212294
• 9G. Cohen, S. Gaubert, J.-P. Quadrat.
  Max-plus algebra and system theory: where we are and where to go now, in: Annual Reviews in Control, 1999, vol. 23, pp. 207–219.
• 10S. Gaubert, J. Gunawardena.
  The Perron-Frobenius Theorem for Homogeneous, Monotone Functions, in: Trans. of AMS, 2004, vol. 356, n^o 12, pp. 4931-4950.
  http://www.ams.org/tran/2004-356-12/S0002-9947-04-03470-1/home.html

Publications of the year

Articles in International Peer-Reviewed Journals

• 11M. Akian, S. Gaubert, A. Hochart.
  Ergodicity conditions for zero-sum games, in: Discrete and Continuous Dynamical Systems - Series A, September 2015, vol. 35, n^o 9, 31 p, See also arXiv: 1405.4658. [ DOI : 10.3934/dcds.2015.35.3901 ]
  https://hal.inria.fr/hal-01096206
• 12M. Akian, S. Gaubert, R. Nussbaum.
  Uniqueness of the fixed point of nonexpansive semidifferentiable maps, in: Transactions of the American Mathematical Society, February 2016, vol. 368, n^o 2. [ DOI : 10.1090/S0002-9947-2015-06413-7 ]
  https://hal.inria.fr/hal-00783682
• 13X. Allamigeon, P. Benchimol, S. Gaubert, M. Joswig.
  Tropicalizing the simplex algorithm, in: Siam Journal on Discrete Mathematics, April 2015, vol. 29, n^o 2, Preprint arXiv:1308.0454, 35 pages, 7 figures, 4 algorithms. Published in SIAM Journal on Discrete Mathematics. [ DOI : 10.1137/130936464 ]
  https://hal.inria.fr/hal-00930913
• 14J. Bolte, S. Gaubert, G. Vigeral.
  Definable Zero-Sum Stochastic Games, in: Mathematics of Operations Research, 2015, vol. 40, n^o 1, pp. 171-191. [ DOI : 10.1287/moor.2014.0666 ]
  https://hal.archives-ouvertes.fr/hal-00777707
• 15S. Gaubert, T. Lepoutre.
  Discrete limit and monotonicity properties of the Floquet eigenvalue in an age structured cell division cycle model, in: Journal of Mathematical Biology, December 2015, vol. 71, n^o 6, 30 pages. [ DOI : 10.1007/s00285-015-0874-3 ]
  https://hal.inria.fr/hal-00773211
• 16S. Gaubert, Z. Qu.
  Dobrushin ergodicity coefficient for Markov operators on cones, in: Integral Equations and Operator Theory, January 2015, vol. 1, n^o 81, pp. 127-150, Also arXiv:1307.4649. [ DOI : 10.1007/s00020-014-2193-2 ]
  https://hal.inria.fr/hal-01099179
• 17S. Gaubert, Z. Qu, S. Sridharan.
  Maximizing concave piecewise affine functions on the unitary group, in: Optimization Letters, September 2015. [ DOI : 10.1007/s11590-015-0951-y ]
  https://hal.inria.fr/hal-01248813
• 18V. Magron, X. Allamigeon, S. Gaubert, B. Werner.
  Formal Proofs for Nonlinear Optimization, in: Journal of Formalized Reasoning, January 2015, vol. 8, n^o 15, pp. 1-24, Also ArXiv:1404.7282.
  https://hal.archives-ouvertes.fr/hal-00985675
• 19A. Niv.
  On pseudo-inverses of matrices and their characteristic polynomials in supertropical algebra, in: Linear Algebra and its Applications, April 2015, vol. 471, pp. 264–290. [ DOI : 10.1016/j.laa.2014.12.038 ]
  https://hal.inria.fr/hal-01253421

Invited Conferences

• 20M. Akian.
  Majorization inequalities for valuations of eigenvalues using tropical algebra, in: 4th International Conference on Matrix methods in Mathematics and Applications (MMMA-2015), Moscow, Russia, August 2015.
  https://hal.inria.fr/hal-01252363
• 21M. Akian, S. Gaubert, A. Hochart.
  Ergodicity Condition for Zero-Sum Games, in: SIAM Conference on Control and its Applications (SIAM CT'15), Paris, France, July 2015.
  https://hal.inria.fr/hal-01252413
• 22M. Akian, S. Gaubert, A. Marchesini, F. Tisseur.
  Hungarian Scaling of Polynomial Eigenproblems , in: SIAM Conference on Applied Linear Algebra (SIAM LA), Atlanta, United States, October 2015.
  https://hal.inria.fr/hal-01252398
• 23X. Allamigeon, P. Benchimol, S. Gaubert.
  Tropicalizing Semialgebraic Pivoting Rules, Or How to Solve Mean Payoff Games in Polynomial Time on Average, in: SIAM Conference on Control and its Applications (SIAM CT’15), Paris, France, July 2015.
  https://hal.inria.fr/hal-01263357
• 24X. Allamigeon, P. Benchimol, S. Gaubert, M. Joswig.
  Long and Winding Central Paths, in: SIAM Conference on Control and its Applications (SIAM CT’15), Paris, France, July 2015.
  https://hal.inria.fr/hal-01263337
• 25A. Marchesini.
  Tropical diagonal scaling for asymptotic eigenvalue problems, in: The 8th International Congress on Industrial and Applied Mathematics (ICIAM), Beijing, China, August 2015.
  https://hal.inria.fr/hal-01253175

International Conferences with Proceedings

• 26M. Akian, S. Gaubert, A. Hochart.
  Hypergraph conditions for the solvability of the ergodic equation for zero-sum games, in: 54th IEEE Conference on Decision and Control (CDC 2015), Osaka, Japan, December 2015.
  https://hal.inria.fr/hal-01249321
• 27M. Akian, S. Gaubert, A. Marchesini.
  Tropical bounds for the eigenvalues of block structured matrices, in: SIAM Conference on Applied Linear Algebra (SIAM LA), Atlanta, United States, October 2015.
  https://hal.inria.fr/hal-01252379
• 28X. Allamigeon, V. Boeuf, S. Gaubert.
  Performance evaluation of an emergency call center: tropical polynomial systems applied to timed Petri nets, in: 13th International Conference, Formal Modeling and Analysis of Timed Systems (FORMATS 2015), Madrid, Spain, Springer, September 2015, vol. 9268. [ DOI : 10.1007/978-3-319-22975-1_2 ]
  https://hal.inria.fr/hal-01248814
• 30A. Hochart, M. Akian, S. Gaubert.
  Generic Uniqueness of the Bias Vector of Mean-Payoff Zero-Sum Games, in: SIAM Conference on Control and its Applications (SIAM CT’15), Paris, France, July 2015.
  https://hal.inria.fr/hal-01263363
• 31N. Stott, X. Allamigeon, S. Gaubert, E. Goubault, S. Putot.
  Eigenvectors of Non-Linear Maps on the Cone of Positive Semidefinite Matrices Application to Stability Analysis, in: SIAM Conference on Control and its Applications (SIAM CT’15), Paris, France, July 2015.
  https://hal.inria.fr/hal-01263384
• 32N. Stott, X. Allamigeon, S. Gaubert.
  Maximal Lower Bounds in the Loewner order, in: 2015 SIAM Conference on Applied Linear Algebra, Atlanta, United States, October 2015.
  https://hal.inria.fr/hal-01263476

Conferences without Proceedings

• 33A. Niv.
  Factorization of tropical matrices, in: Tropical Algebraic Geometry Symposium 2015, Providence, Rhode Island, United States, Brown University, April 2015.
  https://hal.inria.fr/hal-01260232

Other Publications

• 34M. Akian, S. Gaubert, R. Bapat.
  Non-archimedean valuations of eigenvalues of matrix polynomials, May 2015, working paper or preprint.
  https://hal.inria.fr/hal-01251803
• 35X. Allamigeon, R. D. Katz.
  Tropicalization of facets of polytopes, December 2015, 18 pages, 6 figures; v2: major revision.
  https://hal.inria.fr/hal-01096435
• 36Z. Izhakian, A. Niv, L. Rowen.
  Supertropical SLn , August 2015, working paper or preprint.
  https://hal.inria.fr/hal-01253424
• 37A. Niv, L. Rowen.
  Dependence of tropical eigenspaces, January 2016, working paper or preprint.
  https://hal.inria.fr/hal-01253422
• 38C. Walsh.
  Hilbert and Thompson geometries isometric to infinite-dimensional Banach spaces, December 2015, working paper or preprint.
  https://hal.inria.fr/hal-01249343

References in notes

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  Stochastic games and applications, NATO Science Series C: Mathematical and Physical Sciences, Kluwer Academic Publishers, Dordrecht, 2003, vol. 570, x+473 p.
• 40M. Akian, R. Bapat, S. Gaubert.
  Perturbation of eigenvalues of matrix pencils and optimal assignment problem, in: C. R. Acad. Sci. Paris, Série I, 2004, vol. 339, pp. 103–108.
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• 41M. Akian, R. Bapat, S. Gaubert.
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• 42M. Akian, R. Bapat, S. Gaubert.
  Asymptotics of the Perron Eigenvalue and Eigenvector using Max Algebra, in: C. R. Acad. Sci. Paris., 1998, vol. 327, Série I, pp. 927–932.
  http://hal.inria.fr/inria-00073240
• 43M. Akian, S. Gaubert, A. Guterman.
  Linear independence over tropical semirings and beyond, in: Proceedings of the International Conference on Tropical and Idempotent Mathematics, G. Litvinov, S. Sergeev (editors), Contemporary Mathematics, American Mathematical Society, 2009, vol. 495, pp. 1-38.
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• 44M. Akian, S. Gaubert, A. Guterman.
  Tropical polyhedra are equivalent to mean payoff games, in: Internat. J. Algebra Comput., 2012, vol. 22, n^o 1, 1250001, 43 p. [ DOI : 10.1142/S0218196711006674 ]
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• 45M. Akian, S. Gaubert, A. Guterman.
  Tropical Cramer Determinants Revisited, in: Tropical and Idempotent Mathematics and Applications, G. Litvinov, S. Sergeev (editors), Contemporary Mathematics, AMS, 2014, vol. 616, 45 p, See also arXiv:1309.6298.
  https://hal.inria.fr/hal-00881203
• 46M. Akian, S. Gaubert, V. Kolokoltsov.
  Set coverings and invertibility of functional Galois connections, in: Idempotent Mathematics and Mathematical Physics, G. Litvinov, V. Maslov (editors), Contemporary Mathematics, American Mathematical Society, 2005, pp. 19-51.
  http://arxiv.org/abs/math.FA/0403441
• 47M. Akian, S. Gaubert, V. Kolokoltsov.
  Solutions of max-plus linear equations and large deviations, in: Proceedings of the joint 44th IEEE Conference on Decision and Control and European Control Conference ECC 2005 (CDC-ECC'05), Seville, Espagne, 2005.
  http://arxiv.org/abs/math.PR/0509279
• 48M. Akian, S. Gaubert, A. Lakhoua.
  The max-plus finite element method for solving deterministic optimal control problems: basic properties and convergence analysis, in: SIAM J. Control Optim., 2008, vol. 47, n^o 2, pp. 817–848. [ DOI : 10.1137/060655286 ]
  http://www.arxiv.org/abs/math.OC/0603619
• 49M. Akian, S. Gaubert, A. Marchesini.
  Tropical bounds for eigenvalues of matrices, in: Linear Algebra and its Applications, April 2014, vol. 446, pp. 281–303, See also arXiv:1309.7319. [ DOI : 10.1016/j.laa.2013.12.021 ]
  https://hal.inria.fr/hal-00881205
• 50M. Akian, S. Gaubert, M. Sharify.
  Log-majorization of the moduli of the eigenvalues of a matrix polynomial by tropical roots, 2013, Preprint arXiv:1304.2967, 29 pages, 5 figures.
  http://hal.inria.fr/hal-00881196
• 51M. Akian, S. Gaubert, C. Walsh.
  The max-plus Martin boundary, in: Doc. Math., 2009, vol. 14, pp. 195–240.
  http://arxiv.org/abs/math/0412408
• 52M. Akian, J.-P. Quadrat, M. Viot.
  Duality between probability and optimization, in: Idempotency, J. Gunawardena (editor), Publications of the Isaac Newton Institute, Cambridge University Press, 1998.
• 53X. Allamigeon, P. Benchimol, S. Gaubert.
  The tropical shadow-vertex algorithm solves mean payoff games in polynomial time on average, in: ICALP 2014, Copenhagen, France, J. Esparza, P. Fraigniaud, T. Husfeldt, E. Koutsoupias (editors), 41st International Colloquium, ICALP 2014, Copenhagen, Denmark, July 8-11, 2014, Proceedings, Part I, Springer, July 2014, vol. 8572, 12 p. [ DOI : 10.1007/978-3-662-43948-7_8 ]
  https://hal.inria.fr/hal-01096447
• 54X. Allamigeon, P. Benchimol, S. Gaubert, M. Joswig.
  Tropicalizing the simplex algorithm, in: ILAS 2013 - 18th Conference of the International Linear Algebra Society, Providence, RI, United States, June 2013.
  http://hal.inria.fr/hal-00930959
• 55X. Allamigeon, P. Benchimol, S. Gaubert, M. Joswig.
  Tropicalizing the Simplex Algorithm, in: SMAI 2013 - 6ème biennale des mathématiques appliquées et industrielles, Seignosse, France, May 2013, Poster présentant l'article arXiv:1308.0454.
  http://hal.inria.fr/hal-00930941
• 56X. Allamigeon, P. Benchimol, S. Gaubert, M. Joswig.
  Combinatorial simplex algorithms can solve mean payoff games, in: SIAM Journal on Optimization, December 2014, vol. 24, n^o 4, 22 p, Preprint arXiv:1309.5925, 15 pages, 3 figures. [ DOI : 10.1137/140953800 ]
  https://hal.inria.fr/hal-00930915
• 57X. Allamigeon, P. Benchimol, S. Gaubert, M. Joswig.
  Combinatorial Simplex Algorithms Can Solve Mean Payoff Games, in: The 21st International Symposium on Mathematical Theory of Networks and Systems (MTNS 2014), Groningen, Netherlands, July 2014.
  https://hal.inria.fr/hal-01097727
• 58X. Allamigeon, P. Benchimol, S. Gaubert, M. Joswig.
  Combinatorial simplex algorithms can solve mean payoff games, in: 20th Conference of the International Federation of Operational Research Societies, Barcelone, Spain, July 2014.
  https://hal.inria.fr/hal-01097728
• 59X. Allamigeon, P. Benchimol, S. Gaubert, M. Joswig.
  La méthode du simplexe tropical, in: ROADEF - 15ème congrès annuel de la Société française de recherche opérationnelle et d’aide à la décision, Bordeaux, France, Société française de recherche opérationnelle et d’aide à la décision (ROADEF), February 2014, arxiv 1308.0454.
  https://hal.inria.fr/hal-01097726
• 60X. Allamigeon, P. Benchimol, S. Gaubert, M. Joswig.
  Long and winding central paths, May 2014, Preprint arXiv:1405.4161, v2 May 2015.
  https://hal.inria.fr/hal-01096452
• 61X. Allamigeon, S. Gaubert, E. Goubault.
  Inferring Min and Max Invariants Using Max-plus Polyhedra, in: Proceedings of the 15th International Static Analysis Symposium (SAS'08), Springer, 2008, vol. 5079, Valencia, Spain, 16-18 July 2008.
• 62X. Allamigeon, S. Gaubert, E. Goubault.
  The tropical double description method, in: Proceedings of the 27th International Symposium on Theoretical Aspects of Computer Science (STACS'2010), Nancy, France, March 4-6 2010.
  http://drops.dagstuhl.de/opus/volltexte/2010/2443/pdf/1001.AllamigeonXavier.2443.pdf
• 63X. Allamigeon, S. Gaubert, E. Goubault.
  Computing the Vertices of Tropical Polyhedra using Directed Hypergraphs, in: Discrete and Computational Geometry, February 2013, vol. 49, n^o 2, pp. 247-279. [ DOI : 10.1007/s00454-012-9469-6 ]
  http://hal.inria.fr/hal-00782862
• 64X. Allamigeon, R. Katz.
  Minimal external representations of tropical polyhedra, in: Journal of Combinatorial Theory, Series A, 2013, vol. 120, n^o 4, pp. 907-940. [ DOI : 10.1016/j.jcta.2013.01.011 ]
  http://hal.inria.fr/hal-00782837
• 65X. Allamigeon, R. D. Katz.
  Tropicalization of facets of polytopes, August 2014, Preprint arXiv:1408.6176.
  https://hal.inria.fr/hal-01096435
• 66N. Bacaër.
  Perturbations singulières et théorie spectrale min-plus, Université Paris 6, January 2002.
• 67F. Baccelli, D. Hong.
  TCP is max-plus linear and what it tells us on its throughput, in: Proceedings of the conference on Applications, Technologies, Architectures, and Protocols for Computer Communication, 2000, pp. 219-230.
• 68R. Bapat.
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  Tropical aspects of linear programming, Ecole Polytechnique, December 2014.
  https://hal-polytechnique.archives-ouvertes.fr/tel-01198482
• 71A. Benveniste, S. Gaubert, C. Jard.
  Monotone rational series and max-plus algebraic models of real-time systems, in: Proc. of the Fourth Workshop on Discrete Event Systems (WODES98), Cagliari, Italy, IEE, 1998.
• 72A. Berenstein, A. N. Kirillov.
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  Exponential behaviour of the Butkovič-Zimmermann algorithm for solving two-sided linear systems in max-algebra, in: Discrete Appl. Math., 2008, vol. 156, n^o 18, pp. 3506–3509.
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• 74T. Blyth, M. Janowitz.
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• 75F. Bonnans, S. Gaubert.
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• 76H. Braker.
  Algorithms and Applications in Timed Discrete Event Systems, Delft University of Technology, Dec 1993.
• 77S. Burns.
  Performance analysis and optimization of asynchronous circuits, Caltech, 1990.
• 78P. Butkovič.
  Max-algebra: the linear algebra of combinatorics?, in: Linear Algebra and Appl., 2003, vol. 367, pp. 313-335.
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  Incline algebra and applications, Ellis Horwood, 1984.
• 80C.-S. Chang.
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  Algorithmes d'itération sur les politiques pour les applications monotones contractantes, École des Mines, Dec. 2001.
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  A policy iteration algorithm for zero-sum stochastic games with mean payoff, in: C. R. Math. Acad. Sci. Paris, 2006, vol. 343, n^o 5, pp. 377–382.
• 85J. Cochet-Terrasson, G. Cohen, S. Gaubert, M. Mc Gettrick, J.-P. Quadrat.
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