EN FR
EN FR
Bilateral Contracts and Grants with Industry
Bibliography
Bilateral Contracts and Grants with Industry
Bibliography


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, no 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, no 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, no 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, no 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, no 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, no 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, no 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, no 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, no 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, no 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, no 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, no 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, no 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

References in notes
  • 39A. Neyman, S. Sorin (editors)

    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.

    http://www.arxiv.org/abs/math.SP/0402438
  • 41M. Akian, R. Bapat, S. Gaubert.

    Min-plus methods in eigenvalue perturbation theory and generalised Lidskii-Vishik-Ljusternik theorem, 2005.

    http://arxiv.org/abs/math.SP/0402090
  • 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.

    http://www.arxiv.org/abs/0812.3496
  • 44M. Akian, S. Gaubert, A. Guterman.

    Tropical polyhedra are equivalent to mean payoff games, in: Internat. J. Algebra Comput., 2012, vol. 22, no 1, 1250001, 43 p. [ DOI : 10.1142/S0218196711006674 ]

    http://arxiv.org/abs/0912.2462
  • 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, no 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, no 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, no 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, no 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.

    A max version of the Perron-Frobenius theorem, in: Linear Algebra Appl., 1998, vol. 275/276, pp. 3–18.
  • 69R. Bapat, T. Raghavan.

    Nonnegative matrices and applications, Cambridge university press, 1997, no 64, XIII+336 p.
  • 70P. Benchimol.

    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.

    The Robinson-Schensted-Knuth bijection, quantum matrices, and piece-wise linear combinatorics, in: Proceedings of FPSAC'01, 2001.
  • 73M. Bezem, R. Nieuwenhuis, E. Rodríguez-Carbonell.

    Exponential behaviour of the Butkovič-Zimmermann algorithm for solving two-sided linear systems in max-algebra, in: Discrete Appl. Math., 2008, vol. 156, no 18, pp. 3506–3509.

    http://dx.doi.org/10.1016/j.dam.2008.03.016
  • 74T. Blyth, M. Janowitz.

    Residuation Theory, Pergamon press, 1972.
  • 75F. Bonnans, S. Gaubert.

    Recherche opérationnelle: aspects mathématiques et applications, École Polytechnique, 2012, Huitième édition, 180 pages.
  • 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.
  • 79Z. Cao, K. Kim, F. Roush.

    Incline algebra and applications, Ellis Horwood, 1984.
  • 80C.-S. Chang.

    Performance guarantees in Communication networks, Springer, 2000.
  • 81W. Chou, R. Griffiths.

    Ground states of one dimensional systems using effective potentials, in: Phys. Rev. B, 1986, vol. 34, pp. 6219–34.
  • 82P. Chretienne.

    Les Réseaux de Petri Temporisés, Thèse Université Pierre et Marie Curie (Paris VI), Paris, 1983.
  • 83J. Cochet-Terrasson.

    Algorithmes d'itération sur les politiques pour les applications monotones contractantes, École des Mines, Dec. 2001.
  • 84J. Cochet-Terrasson, S. Gaubert.

    A policy iteration algorithm for zero-sum stochastic games with mean payoff, in: C. R. Math. Acad. Sci. Paris, 2006, vol. 343, no 5, pp. 377–382.
  • 85J. Cochet-Terrasson, G. Cohen, S. Gaubert, M. Mc Gettrick, J.-P. Quadrat.

    Numerical computation of spectral elements in max-plus algebra, in: Proc. of the IFAC Conference on System Structure and Control, Nantes, July 1998.
  • 86G. Cohen, D. Dubois, J.-P. Quadrat, M. Viot.

    Analyse du comportement périodique des systèmes de production par la théorie des dioïdes, Inria, Le Chesnay, France, 1983, no 191.

    http://hal.inria.fr/inria-00076367
  • 87J.-P. Comet.

    Application of max-plus algebra to biological sequence comparison, in: Theor. Comput. Sci., Special issue on max-plus algebras, 2003, vol. 293, pp. 189–217.
  • 88A. Costan, S. Gaubert, E. Goubault, M. Martel, S. Putot.

    A policy iteration algorithm for computing fixed points in static analysis of programs, in: Proceedings of the 17th International Conference on Computer Aided Verification (CAV'05), Edinburgh, LNCS, Springer, July 2005, pp. 462–475.
  • 89P. Cousot, R. Cousot.

    Abstract Interpretation: A unified lattice model for static analysis of programs by construction of approximations of fixed points, in: Principles of Programming Languages 4, 1977, pp. 238–252.
  • 90P. Cousot, R. Cousot.

    Comparison of the Galois connection and widening/narrowing approaches to abstract interpretation. JTASPEFL'91, Bordeaux, in: BIGRE, October 1991, vol. 74, pp. 107–110.
  • 91M. Crandall, L. Tartar.

    Some relations between non expansive and order preserving maps, in: Proceedings of the AMS, 1980, vol. 78, no 3, pp. 385–390.
  • 92R. Cuninghame-Green.

    Minimax Algebra, Lecture notes in Economics and Mathematical Systems, Springer, 1979, no 166.
  • 93J. De Loera, B. Sturmfels, C. Vinzant.

    The central curve in linear programming, in: Foundations of Computational Mathematics, 2012, vol. 12, no 4, pp. 509–540.
  • 94J.-P. Dedieu, G. Malajovich, M. Shub.

    On the Curvature of the Central Path of Linear Programming Theory, in: Foundations of Computational Mathematics, 2005, vol. 5, no 2, pp. 145–171.
  • 95P. Del Moral.

    Maslov optimization theory: topological aspects, in: Idempotency (Bristol, 1994), Cambridge, Publ. Newton Inst., Cambridge Univ. Press, 1998, vol. 11, pp. 354–382.
  • 96P. Del Moral, T. Thuillet, G. Rigal, G. Salut.

    Optimal versus random processes : the nonlinear case, LAAS, 1990.
  • 97M. Develin, B. Sturmfels.

    Tropical convexity, in: Doc. Math., 2004, vol. 9, pp. 1–27.
  • 98M. Develin, J. Yu.

    Tropical polytopes and cellular resolutions, in: Experimental Mathematics, 2007, vol. 16, no 3, pp. 277–292.

    http://arxiv.org/abs/math/0605494
  • 99A. Deza, T. Terlaky, Y. Zinchenko.

    Polytopes and arrangements: diameter and curvature, in: Operations Research Letters, 2008, vol. 36, no 2, pp. 215–222.
  • 100A. Deza, T. Terlaky, Y. Zinchenko.

    Central path curvature and iteration-complexity for redundant Klee-Minty cubes, in: Advances in applied mathematics and global optimization, New York, Adv. Mech. Math., Springer, 2009, vol. 17, pp. 223–256.

    http://dx.doi.org/10.1007/978-0-387-75714-8_7
  • 101V. Dhingra, S. Gaubert.

    How to solve large scale deterministic games with mean payoff by policy iteration, in: Valuetools '06: Proceedings of the 1st international conference on Performance evaluation methodologies and tools, New York, NY, USA, ACM Press, 2006, 12 p.

    http://doi.acm.org/10.1145/1190095.1190110
  • 102M. Di Loreto, S. Gaubert, R. Katz, J.-J. Loiseau.

    Duality between invariant spaces for max-plus linear discrete event systems, in: SIAM J. Control Optim., 2010, vol. 48, no 8, pp. 5606-5628.

    http://arxiv.org/abs/0901.2915
  • 103M. Dubreil-Jacotin, L. Lesieur, R. Croisot.

    Leçons sur la Théorie des Treillis, des Structures Algébriques Ordonnées, et des Treillis géométriques, Cahiers Scientifiques, Gauthier Villars, Paris, 1953, vol. XXI.
  • 104A. Fahim, N. Touzi, X. Warin.

    A probabilistic numerical method for fully nonlinear parabolic PDEs, in: Ann. Appl. Probab., 2011, vol. 21, no 4, pp. 1322–1364.

    http://dx.doi.org/10.1214/10-AAP723
  • 105N. Farhi, M. Goursat, J.-P. Quadrat.

    Derivation of the Fundamental Diagram for Two Circular Roads and a Crossing Using Minplus Algebra and Petri Net Modeling, in: Proceedings of the joint 44th IEEE Conference on Decision and Control and European Control Conference ECC 2005 (CDC-ECC'05), Seville, Espagne, 2005.
  • 106A. Fathi.

    Solutions KAM faibles et théorie de Mather sur les systèmes lagrangiens, in: C. R. Acad. Sci. Paris, Sér. I Math., 1997, vol. 324, no 9, pp. 1043–1046.
  • 107S. Fomin, A. Zelevinsky.

    Cluster algebras. I. Foundations, in: J. Amer. Math. Soc., 2002, vol. 15, no 2, pp. 497–529.

    http://arxiv.org/abs/math.RT/0104151
  • 108S. Friedland.

    Limit eigenvalues of nonnegative matrices, in: Linear Algebra and Its Applications, 1986, vol. 74, pp. 173–178.

    http://dx.doi.org/10.1016/0024-3795(86)90120-5
  • 109S. Gaubert.

    Performance Evaluation of (max,+) Automata, in: IEEE Trans. on Automatic Control, Dec 1995, vol. 40, no 12, pp. 2014–2025.
  • 110S. Gaubert, E. Goubault, A. Taly, S. Zennou.

    Static Analysis by Policy Iteration in Relational Domains, in: Proceedings of the Proc. of the 16th European Symposium on Programming (ESOP'07), Braga (Portugal), LNCS, Springer, 2007, vol. 4421, pp. 237–252.

    http://dx.doi.org/10.1007/978-3-540-71316-6_17
  • 111S. Gaubert, J. Gunawardena.

    The Duality Theorem for min-max functions, in: C. R. Acad. Sci. Paris., 1998, vol. 326, Série I, pp. 43–48.
  • 112S. Gaubert, R. Katz.

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